跳到正文
研踪PaperTrail

YOUR RESEARCH, IN SIGHT

让下一篇重要论文，不再错过。

覆盖计算机全学科，以 AI 为快捷入口。关注方向、作者和关键词，把发现变成持续的研究积累。

部分采集异常
正在读取账号与研究记录…

全站更新概况

+1072新增论文
+845其中 AI 相关
+94已有论文修订
+100新增 AI 导读

arXiv 最近完成扫描：2026-11-09 21:43 · 全站最近入库：2026-11-09 13:22各信源进度 →

统计口径与数据新鲜度

统计 2026-11-08 21:46 — 2026-11-09 21:46（北京时间） · 点击数字查看对应简报；AI 相关包含在新增论文内。

最近完成检查：2026-11-09 21:43最近发现新增版本：2026-11-09 13:22库内论文最新更新时间：2026-11-07 02:59

每分钟刷新已保存的数据。空检查不代表采集异常；新收录可能包含历史论文。AI 导读按新增版本计数。

18,172 已收录论文15,506 AI 相关4,527 有修订112 HF 社区发现

浏览论文库

研究日报 / 周报 →按信源浏览 →

时间范围跟随排序：版本更新、本站收录或首次发表。最新收录可能包含历史论文。部分信源异常，查看状态 →

找到 486 篇论文 · 按版本更新时间排序上轮扫描起点 2026-11-09 21:40（北京时间）
版本更新 · v4arXiv:2607.15530

On the Role of Normalization in Binary Iterative Hard Thresholding for 1-bit Compressed Sensing

Arya Mazumdar, Prateeti Mukherjee

原文摘要

Binary Iterative Hard Thresholding (BIHT) is a simple, yet effective, greedy method for recovering a sparse vector from one-bit sign measurements. In its original form, BIHT performs a ``gradient-descent'' step, followed by hard thresholding. A convergence analysis of this algorithm was left open in the introductory work of Jacques, Laska, Boufounos, and Baraniuk [IEEE Trans. Inform. Theory (2013)] and has remained unresolved for over a decade, with subsequent sharp analyses studying a normalized variant instead, that additionally projects every iterate onto the unit sphere. This paper resolves that gap and characterizes when per-iterate normalization is algorithmically necessary. In the noiseless setting, we prove a universal, sample-optimal convergence theorem for the original BIHT algorithm. Specifically, with $\widetilde O(s/ε)$ measurements, a deterministic, computable finite-time iterate has directional error at most $ε$, simultaneously for every $s$-sparse unit vector. This matches the optimal sample dependence achieved by normalized BIHT in prior work. Under sign corruptions, we prove a sharp separation. If at most a $τ$ fraction of signs are flipped adversarially, then BIHT, without per-iterate normalization, still reaches the robust error floor at an early iterate with a matching $\widetilde O(s/ε)$ sample complexity rate as its normalized variant. This recovery, however, is not stable. We prove a scalar lower bound showing that any nontrivial corruption pattern, even one that involves only one flipped sign together with one clean sign, forces the iterates to oscillate indefinitely. Consequently, no general last-iterate convergence theorem can hold for BIHT under sign corruptions, while its normalized surrogate provably escapes this instance.

cs.IT · cs.DS · math.ST · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2604.07794

Density Decomposition on Hypergraphs

Xiaoyu Leng, Hongchao Qin, Rong-Hua Li, Guoren Wang

原文摘要

Hypergraphs capture higher-order interactions involving multiple entities. Existing decomposition models, such as $k$-core and nbr-$k$-core, rely on degree or neighborhood constraints and may overlook fine-grained density variations. We propose a $(k,δ)$-dense subhypergraph model based on capped hyperedge contributions. For each parameter pair, the unique dense set is the inclusionwise smallest maximizer of a penalized capped hyperedge contribution. These dense sets form a nested hierarchy characterized by egalitarian $δ$-orientations and hypergraph reachability. We develop three algorithms for dense subhypergraph search and two for complete density decomposition. Both decomposition algorithms use integral flow balancing: Flow-Decomp extracts density levels through strongly connected component condensation, while Reverse-Decomp uses direct reverse propagation. Once an egalitarian orientation is obtained, both recover all density levels in linear time. We further derive sandwich bounds that restrict computation to equivalent residual subproblems and develop incremental algorithms for maintaining the hierarchy under hyperedge insertions and deletions. Experiments on nine real-world hypergraphs, including datasets with over 15 million vertices, compare our methods with four established decomposition models. The results show that Reverse-Decomp improves decomposition efficiency, incremental maintenance outperforms recomputation in the tested settings, and the proposed model captures density structures overlooked by degree-based decompositions.

cs.SI · cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38206

Averaged Annealed Markov Chains Achieve the Algorithmic Threshold for Tensor PCA, Part II: Langevin Dynamics

Aniket Das, Tselil Schramm

原文摘要

We consider the tensor principal components analysis (tensor PCA) problem on the sphere, in which we are asked to recover an unknown vector in $\mathcal{S}_N=\{x\in\mathbb{R}^N:\lVert x\rVert^2=N\}$ from a noisy observation of its $k$-th tensor power, for a fixed $k\ge3$. Tensor PCA exhibits a well-studied information-computation gap: global algorithms such as spectral methods and sum-of-squares work above an algorithmic threshold, below which we know matching lower bounds (against these and some other restricted models of computation). In contrast, local algorithms such as Markov chains were only known to succeed from a random initialization at a polynomially larger signal-to-noise ratio, and were believed to be inferior to global algorithms for tensor PCA. Continuing the program initiated in Part I [arXiv:2610.16705], we show that spherical Langevin dynamics, when supplemented with annealing and ergodic averaging, achieves polynomial-time strong recovery above the algorithmic threshold from a uniformly random initialization. Together with Part I, our results demonstrate that local Markov chains can succeed all the way down to the algorithmic threshold from an uninformative cold start.

cs.LG · cs.DS · math.PR · math.ST

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38205

Fast Sparse $α$-Navigable Graph Construction with Improved Resource Augmentation

Alex Conway, Laxman Dhulipala, Martin Farach-Colton, Ben Landrum, Christopher Musco, Yarin Shechter, Torsten Suel, Richard Wen

原文摘要

Graph-based nearest neighbor search methods, which run greedy search on a directed graph over the data points, have surged in popularity in recent years. A common goal is to construct a search graph with the $α$-navigability property, which ensures that greedy search returns provably good approximate nearest neighbors and converges in few iterations. Increasing $α\geq 1$ improves accuracy and convergence rate, but requires more edges, which increases both space and search time. This tradeoff has motivated the study of algorithms for constructing a sparsest $α$-navigable graph for a given set of points. For any point set and any distance function, we show how to compute an $α$-navigable graph with at most $O(\log n)$ times as many edges as the sparsest $(1+\varepsilon)α$-navigable graph, in $O(n^ω\log(Δ)/\varepsilon)$ time, where $ω< 2.372$ is the matrix multiplication exponent and $Δ$ is the aspect ratio of the input. This improves on Khanna, Padaki, and Waingarten (SODA 2026), who achieve the same runtime but are only competitive with the sparsest $2(1+\varepsilon)α$-navigable graph. Since sparsity often increases rapidly with $α$ (typically $α\leq 1.1$), their bound can be significantly weaker. Previously, the best algorithm competing with the sparsest $(1+\varepsilon)α$-navigable graph required $\widetilde{O}(n^{2.5})$ time. Our techniques also extend to constructing sparse $τ$-monotonic graphs, another popular target in nearest neighbor search. Finally, we give a fine-grained complexity analysis suggesting that improving the $O(n^ω)$ running time is unlikely, or would require a very different approach. It is based on hardness results for problems related to verifying whether a graph is navigable, a topic of independent interest.

cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38164

Separations between $\#\mathrm{BIS}$ and $\#\mathrm{IS}$

Ijay Narang

原文摘要

We give complexity-theoretic separations between $\#\mathrm{BIS}$ and $\#\mathrm{IS}$. Given a graph $G$, and a fugacity $λ>0$, the hard-core model is given by $Z_G(λ)=\sum_{I\in\mathcal I(G)}λ^{|I|}$, where $\mathcal I(G)$ denotes the independent sets of $G$. For $F\ge1$, an $F$-factor approximation to $Z_G(λ)$ is an estimate $\widehat Z$ satisfying $F^{-1}Z_G(λ)\le\widehat Z\le FZ_G(λ)$. Let $\mathcal G_Δ$ denote the class of $Δ$-regular graphs and $\mathcal G_{Δ,Δ}$ the class of $Δ$-regular bipartite graphs. We give two separation results. (1) There exist an integer $Δ\ge3$, a sufficiently large fugacity $λ$, and a constant $c>0$ so that the following hold: (a) For every $δ\in(0,1)$, deterministic $(1+δ)$-factor approximation on $\mathcal G_{Δ,Δ}$ is possible in time $\exp(cn)\operatorname{poly}(n,1/δ)$. (b) Under the Gap-Exponential Time Hypothesis, there exists no deterministic algorithm running in time $\exp(2cn)\operatorname{poly}(n)$ on $\mathcal G_Δ$ that gives an $\frac{11}{10}$-factor approximation. (2) For every fixed $Δ\ge3$ and $\varepsilon\in(0,1)$, for all sufficiently large fugacities $λ$, the following hold: (a) There exists an algorithm which outputs a deterministic $(1+\varepsilon)^n$-factor approximation to $Z_G(λ)$ on $\mathcal G_{Δ,Δ}$ in polynomial time. (b) Under the assumption $\mathrm P\ne\mathrm{NP}$, there exists no deterministic polynomial-time algorithm on $\mathcal G_Δ$ that gives a $(1+\varepsilon)^n$-factor approximation. Both our algorithmic results follow from a new spanning-tree encoding of independent sets that enables an efficient representation of large independent sets.

cs.CC · cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38133

On Worst-Case Guarantees for Graph-Based Nearest-Neighbor Search

Majid Daliri, Mohammadreza Daneshvaramoli, Purna Dutta, Edo Liberty, Cameron Musco, Christopher Musco, Torsten Suel

原文摘要

Graph-based nearest neighbor search algorithms like HNSW, DiskANN, NSG, and others have surged in popularity in recent years due to their excellent empirical performance in comparison to space-partitioning methods like IVF data structures and Locality Sensitive Hashing (LSH). However, in contrast to LSH and related methods, obtaining strong worst-case theoretical guarantees for graph-based search has proven challenging. In this paper, we prove a strong lower bound that helps explain the lack of progress towards such guarantees. We show that no standard graph-based method (any that runs a variant of greedy search on a flat or hierarchical graph) can achieve sublinear query time for approximate nearest neighbor search in Euclidean space, even for an arbitrarily large approximation factor. On the other hand, we prove that sublinear query time is possible if we allow for Steiner points in the search graph. We obtain bounds comparable to LSH, showing e.g., that graph-based search with Steiner points can solve $c$-approximate nearest neighbor search in Euclidean space with query time $\tilde{O}(n^{1/(c-1)})$. We complement this result with initial experiments exploring how Steiner points can be incorporated into practical graph-based methods.

cs.DS · cs.LG

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38114

Output-Sensitive Enumeration of Maximal Closed Substrings in Linear Space

Johannes Fischer, Dominik Köppl

原文摘要

We revisit the output-sensitive enumeration of maximal closed substrings (MCSs). Given a string of length $n$ over an integer alphabet, let $k$ denote its number of MCS occurrences. We combine a right-to-left sweep on the string with range-successor queries to obtain all MCSs with two deterministic word-RAM bounds: for any fixed $\varepsilon>0$, we can report all MCSs in $O(n\sqrt{\log n}+k\log^\varepsilon n)$ time using $O(n)$ words of space, or in $O(n\sqrt{\log n}+k\log\log n)$ time using $O(n\log\log n)$ words. Both bounds include preprocessing and report occurrences by their endpoints. In particular, these algorithms improve the known $O(n\log n)$ worst-case time bound for sufficiently small output.

cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2510.11547

Sublinear Algorithms for Estimating Single-Linkage Clustering Costs

Pan Peng, Christian Sohler, Yi Xu

原文摘要

Single-linkage clustering (SLC) is a fundamental method for hierarchical data analysis. In the distance setting, a $k$-clustering produced by SLC can be obtained by computing a minimum spanning tree (MST) and deleting its $k-1$ heaviest edges. This naturally induces a cost profile for the SLC hierarchy: for each $k\in[n]$, we define $\mathrm{cost}_k$ to be the weight of the resulting $k$-component spanning forest, equivalently, the minimum total weight of any spanning forest with exactly $k$ connected components. The corresponding \emph{SLC cost profile} is $(\mathrm{cost}_1,\ldots,\mathrm{cost}_n)$, and the scalar quantity $\mathrm{cost}(G)=\sum_{k=1}^{n}\mathrm{cost}_k$ is the area under this profile. We study the problem of approximating these quantities in sublinear time. We assume that the input is a weighted graph $G$ of average degree $d$ with edge weights in $\{1,\dots,W\}$, accessed through adjacency-list queries; missing edges are treated as having infinite distance. Our main result is a sampling-based algorithm that outputs a succinct sketch of the entire SLC cost profile in the distance setting. The algorithm runs in $\widetilde{O}(d\sqrt{W}/\varepsilon^3)$ time and returns a sketch from which one can derive estimates $(\widehat{\mathrm{cost}}_1,\ldots,\widehat{\mathrm{cost}}_n)$ satisfying $\sum_{k=1}^{n}\bigl|\widehat{\mathrm{cost}}_k-\mathrm{cost}_k\bigr| \le \varepsilon\,\mathrm{cost}(G)$. Thus, we obtain an $\ell_1$ approximation to the full profile whose error is at most an $\varepsilon$-fraction of the area under the true profile. In particular, this yields a $(1\pm\varepsilon)$-approximation to $\mathrm{cost}(G)$ within the same running time. We also prove a nearly matching lower bound of $Ω(d\sqrt{W}/\varepsilon^2)$ queries for estimating $\mathrm{cost}(G)$.

cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v4arXiv:2310.18786

A Competitive Algorithm for Agnostic Active Learning

Eric Price, Yihan Zhou

原文摘要

For some hypothesis classes and input distributions, active agnostic learning needs exponentially fewer samples than passive learning; for other classes and distributions, it offers little to no improvement. The most popular algorithms for agnostic active learning express their performance in terms of a parameter called the disagreement coefficient, but it is known that these algorithms are inefficient on some inputs. We take a different approach to agnostic active learning, getting an algorithm that is competitive with the optimal algorithm for any binary hypothesis class $H$ and distribution $D_X$ over $X$. In particular, if any algorithm can use $m^*$ queries to get $O(η)$ error, then our algorithm uses $O(m^* \log |H|)$ queries to get $O(η)$ error. Our algorithm lies in the vein of the splitting-based approach of Dasgupta [2004], which gets a similar result for the realizable ($η= 0$) setting. We also show that it is NP-hard to do better than our algorithm's $O(\log |H|)$ overhead in general.

cs.LG · cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37977

A Simple Optimistic B-Skiplist Algorithm

Jianting Guo, Yicong Luo, Helen Xu

原文摘要

We present the first optimistic concurrent B-skiplist, built on optimistic lock coupling (OLC). OLC replaces the multi-cache-line RW lock with a compact, single-cache-line lock: readers validate a version number without writing to shared memory, avoiding cache invalidations and retrying only on a detected conflict. Although OLC was thought poorly suited to skiplists, where a single per-element lock may span structurally unrelated levels, the B-skiplist's blocked layout places each level (and associated lock) in its own node. We exploit the B-skiplist's upfront knowledge of promotion height with a hybrid top-down scheme that traverses upper levels optimistically and locks only from the promotion level down, so most inserts never dirty a cache line. On 128 threads, the proposed optimistic B-skiplist achieves $1.2-10\times$ higher throughput over state-of-the-art concurrent skiplist implementations. Furthermore, the optimistic B-skiplist achieves $0.8-4.3\times$ the throughput compared to high-performance optimistic B+-tree implementations based on RW locks and OLC. Finally, the optimistic B-skiplist achieves up to $13\times$ lower latency than concurrent skiplists and tree-based indices, and is within $1.6\times$ of the latency of the OLC-based B+-tree.

cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37783

Generating pivot Gray codes for spanning arborescences of complete digraphs and split digraphs in constant amortized time

Bowie Liu, Dennis Wong

原文摘要

We present the first known efficient algorithm to generate pivot Gray codes for spanning arborescences of complete digraphs, listing all spanning arborescences such that consecutive arborescences differ by reassigning the outgoing edge of exactly one vertex. Our recursive algorithm generates each spanning arborescence in constant amortized time using $O(n^2)$ space. We then extend our algorithm to generate the first known pivot Gray codes for spanning arborescences of split digraphs, achieving constant amortized time per arborescence using $ O(n^2) $ space. Finally, we further generalize our approach to proper interval digraphs. When the arborescences are rooted at the leftmost interval, our algorithm generates the pivot Gray code in constant amortized time per arborescence using $ {O}(n^2) $ space.

cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.18220

Approximate Envy-Freeness and Pareto Optimality Beyond Additivity

Harish Chandramouleeswaran, Prajakta Nimbhorkar

原文摘要

We study the compatibility of envy-freeness up to one good (EF1) and Pareto optimality (PO) beyond additive valuations. For two agents with monotone submodular valuations, we prove that a $2/3$-EF1+PO allocation always exists, while for every $α>3/4$, an $α$-EF1+PO allocation may fail to exist even for unweighted coverage valuations. A six-good EF1+PO counterexample resolves the longstanding exact existence question negatively. Exact EF1+PO does exist when one agent has a monotone submodular valuation and the remaining agents have identical additive valuations. For two agents, we also establish tight EF$k$+PO item thresholds of $4k+1$, $2k+1$, and $3k+1$ for two submodular agents, two subadditive agents, and one subadditive and one additive agent, respectively. Finally, deciding whether an EF$k$+PO allocation exists is NP-hard for every fixed integer $k\ge1$, even for three agents with unweighted coverage valuations, one of whom has an additive valuation.

cs.GT · cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37630

Approximate Counting for Mixed $p$-Spin Glasses in Weak External Fields via Cluster Expansion

Qiang Wu

原文摘要

We give algorithms for approximating the partition function $Z_N$ of the Sherrington--Kirkpatrick (SK) model and finite mixed Ising $p$-spin models with $p\ge 3$. The algorithms apply at a fixed margin below the second-moment threshold $β_{\mathrm f}$ with homogeneous weak external fields $|h|\leqρ_0N^{-1/4}$, for fixed $ρ_0>0$. For any accuracy $\varepsilon\in(0,1)$ and failure parameter $δ\in(0,1)$, they approximate $\log Z_N$ to additive error $\varepsilon$. The number of exact operations is polynomial jointly in $N$, $\varepsilon^{-1}$, and $δ^{-1}$. The disorder variables have i.i.d symmetric distribution with unit variance. The failure probability is at most $δ$ plus an explicit disorder tail bound. This tail bound tends to zero under a finite fourth moment condition. Our approach builds on the cluster expansions of Aizenman--Lebowitz--Ruelle~\cite{ALR87} and Dey--Wu~\cites{DW23,DW26}. For higher-order mixtures, we retain hypergraphs using few vertices and evaluate their total weight deterministically through local spin averages and inclusion--exclusion. For SK, we impose cutoffs on the number of vertices of degree at least three and on the total number of edges. We estimate the retained sum using randomized color coding~\cite{AYZ95}. A lower tail control based on reverse hypercontractivity~\cite{MOS13} converts the mean-square approximation of the normalized partition function into logarithmic accuracy.

math.PR · cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2507.16648

An Unconditional Lower Bound for the Active-Set Method in Almost-Linear Programming

Eleon Bach, Yann Disser, Sophie Huiberts, Nils Mosis

原文摘要

We prove that, for every fixed $ε\in(0,1]$, the active-set method requires exponentially many iterations in the worst case to maximize a convex objective of the form $(x_1)^{1+ε}+\vec c^{\top}\vec x$ subject to linear constraints, regardless of the pivot rule used. Our lower bound therefore holds for objectives arbitrarily close to the linear case $ε=0$, where the active-set method coincides with the simplex method and a lower bound for all pivot rules would constitute a major breakthrough. The special case $ε=1$ yields a lower bound in convex quadratic maximization. This improves on the best previously known lower bound [IPCO 2025] requiring polynomial objectives of degree $ω(\log d)$ in dimension $d$ and firmly resolves the open question of whether a constant degree suffices. Our result is based on a novel extended formulation, recursively constructed using deformed products. Its key feature is that it projects onto a polygonal approximation of a parabola while preserving all of its exponentially many vertices. We define a convex objective with a single non-linear variable that forces the active-set method to follow the parabolic boundary of this projection, without allowing any shortcuts along chords corresponding to edges of its full-dimensional preimage.

cs.DM · cs.CC · cs.DS · math.CO

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.10697

A Better Analysis For PPSZ For 3-SAT

Tao Jiang, Shaowei Cai

原文摘要

The PPSZ algorithm of Paturi, Pudlák, Saks, and Zane solves 3-SAT by processing the variables in a uniformly random order, setting a variable whenever a bounded number of clauses implies its value, and guessing it otherwise. Its running time is determined by how many variables are forced in this process, and the exact exponent is a central question in the study of exponential-time satisfiability algorithms. Scheder showed that the classical analysis of PPSZ is not tight for 3-SAT. We ask how much further a sharper analysis of the unmodified algorithm can go. Our analysis uses auxiliary distributions on variable orderings that correlate the positions of variables sharing critical clauses. Such correlations make forcing more likely for some variables, can make it less likely for others, and incur an entropy cost. We choose the correlated pairs at random on short components, so that every pair is selected with the same probability, and we express the forcing loss as a sum of weights attached to these pairs in advance. Gains and losses then scale by the same factor and can be compared directly. Combining the resulting estimate with the complementary estimate of Scheder through an explicit linear-programming certificate gives a uniform improvement for every uniquely satisfiable formula. We prove that the original PPSZ algorithm, with a sufficiently large but fixed implication strength, solves Unique-3-SAT in randomized time $O^*(1.306969598^n)$. Through the lifting framework of Scheder and Steinberger, it solves general 3-SAT in randomized time $O^*(1.307031578^n)$. Both bounds improve the guarantees obtained from the analysis of Scheder for the same algorithm. These improvements follow entirely from the analysis, while PPSZ continues to use a uniformly random variable order and unbiased guesses. It shows that the known guarantees for PPSZ can be strengthened by analysis alone.

cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37361

Online Interval Selection with Binary Predictions: Optimal Consistency and a Continuous Robustness Tradeoff

Zhong Han

原文摘要

We study online interval selection with binary predictions of membership in a final optimal solution. Requests arrive in arbitrary order; accepted requests may be revoked, but rejected or revoked requests cannot be recovered. With rewards proportional to interval length, the best consistency under finite strict robustness is $d=(3+\sqrt5)/2$ when both guarantees hold almost surely on each fixed input, including for randomized algorithms. A continuous lower bound forces consistency strictly above $d$ at every robustness budget below $4\varphi+3\approx9.472$, whereas our deterministic algorithm attains $d$ with exact robustness $\varphi^5\approx11.090$, where $\varphi=(1+\sqrt5)/2$. Each held interval inherits a ledger recording positive prediction mass lost through irrevocable decisions. A tunable replacement cost gives a continuous family with exact consistency throughout and exact robustness on two parameter intervals, including $(C,R)=(25/9,10)$ and $(4,7)$. Randomization permits expected consistency approaching one with finite expected robustness, whereas almost-sure robustness forces expected consistency strictly above two at every finite budget.

cs.DS · cs.LG

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37295

A Linear Kernel for Planar Semitotal Domination

Paloma T. de Lima, Lukas Retschmeier

原文摘要

A set of vertices $S$ in a graph $G$ is a semitotal dominating set if $S$ is a dominating set and every vertex in $S$ has a witness, that is, another vertex in $S$ within distance at most two. The Semitotal Domination problem asks whether $G$ admits such a set of size at most $k$. We study this problem parameterized by the solution size. We provide a linear kernel of size $358k$ on planar graphs, a result that adds to several existing linear kernels for other domination variants on planar graphs. Additionally, we show Semitotal Domination is $W[2]$-hard on split graphs, on bipartite graphs and on $t$-claw-free graphs, it is $W[1]$-hard on circle graphs.

cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:1909.12353

Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm

Gabriel Istrate, Cosmin Bonchis, Mircea Marin

原文摘要

We analyze the expected running time of WalkSAT, a well-known local search procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT problem. We obtain estimates of this expected running time by reducing the problem to a setting amenable to classical techniques from drift analysis. A crucial ingredient of this reduction is the definition of (new, explosive) hypergraph versions of interacting particle systems, notably of coalescing and annihilating random walks as well as the voter model. The use of these tools allows to show that the expected running time of WalkSAT depends on structural parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.

cs.DS · cs.DM · math.CO · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2407.04898

Nash Incentive-compatible Online Mechanism Learning via Weakly Differentially Private Online Learning

Joon Suk Huh, Kirthevasan Kandasamy

原文摘要

We study a multi-round mechanism design problem, where we interact with a set of agents over a sequence of rounds. We wish to design an incentive-compatible (IC) online learning scheme to maximize an application-specific objective within a given class of mechanisms, without prior knowledge of the agents' type distributions. Even if each mechanism in this class is IC in a single round, if an algorithm naively chooses from this class on each round, the entire learning process may not be IC against non-myopic buyers who appear over multiple rounds. On each round, our method randomly chooses between the recommendation of a weakly differentially private online learning algorithm (e.g., Hedge), and a commitment mechanism which penalizes non-truthful behavior. Our method is IC and achieves $O(T^{\frac{1+h}{2}})$ regret for the application-specific objective in an adversarial setting, where $h$ quantifies the long-sightedness of the agents. When compared to prior work, our approach is conceptually simpler,it applies to general mechanism design problems (beyond auctions), and its regret scales gracefully with the size of the mechanism class.

cs.GT · cs.CR · cs.DS · cs.LG

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.23364

Power of Conditional Sampling on Hypergraphs

Debarshi Chanda, Buddha Dev Das, Arijit Ghosh, Gopinath Mishra

原文摘要

Let $G=(V,E)$ be a $d$-uniform hypergraph with $|V|=n$ and $|E|=m$. Estimating $m$ from uniformly random hyperedge samples requires $Θ(\sqrt{m})$ samples by a birthday-paradox argument. We investigate the power of conditional sampling through a hierarchy of oracles: for an integer $1\le s\le d$, given pairwise disjoint subsets $X_1,\ldots,X_s\subseteq V$, the $s$-colorful oracle returns a hyperedge chosen uniformly at random from all hyperedges contained in $X_1\cup\cdots\cup X_s$ that intersect every $X_i$, provided one exists. For $s=1$, this samples a uniformly random hyperedge induced by $X_1$. For every $1\le s\le d$, we give a randomized algorithm that outputs $\widehat{m}\in[(1-\varepsilon)m,(1+\varepsilon)m]$ with probability at least $2/3$ using $O_{s,d}(\operatorname{poly}(1/\varepsilon,\log n))$ conditional samples, where the exponent of $\log n$ is an absolute constant independent of both $s$ and $d$. Conditional sampling thus yields an exponential separation over uniform hyperedge sampling. We also study the decision version, in which the oracle only reports whether a qualifying hyperedge exists. For every $1\le s<d$, we prove that any algorithm using the $s$-colorful decision oracle requires $\widetildeΩ_{s,d}(n^{\frac{d-s}{d-s+1}})$ queries. Hence, for $s<d$, access to uniformly random witness hyperedges (random certificates) is exponentially more powerful than existence queries. For $s=d$, decision queries alone achieve $\operatorname{poly}(1/\varepsilon,\log n)$ query complexity, but the exponent of $\log n$ is known to be $Θ(d)$. The colorful hierarchy thus exhibits a phase transition at $s=d$: for $s<d$, random certificates are essential for polylogarithmic-query estimation, whereas at $s=d$ decision queries suffice, yet random certificates still provably reduce the exponent of $\log n$ from $Θ(d)$ to an absolute constant.

cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2610.28930

Amplified Pruning and Path Selectors for Deterministic Radio Gossiping

Qin Xin

原文摘要

We study deterministic gossiping in unknown strongly connected directed radio networks with $n$ vertices, $m$ arcs, and distinct identifiers in $[N]$, where $N=n^{\mathcal O(1)}$. Messages are unrestricted and collision detection is unavailable. Our neighborhood-clearing procedure reuses an elected receiver to secure its entire closed in-neighborhood in $\mathcal O(n\log^2n\log\log n)$ rounds. Charging each distinct closed neighborhood once yields $\mathcal O(m\log^2n\log\log n)$ rounds under an explicit degree-concentration condition, for every polynomial identifier range. A complementary adaptive-pruning procedure combines quadratic contraction with completion sensitive to the number of unsecured sources. If $a\ge1$ sources remain at completion entry, permutation selectors reduce the balanced completion budget by a factor of $\log^{2/3}(a+1)$ relative to interleaved path selectors. A geometric execution attains $\widetilde{\mathcal O}(k^2+nτ+\min\{u^2,(nu)^{2/3}\})$ for a path cover of scale $k$, weight $τ$, and $u$ exceptions. For directed graphs with common in- and out-degree $Δ$, the portfolio achieves $\widetilde{\mathcal O}(\min\{n\sqrtΔ,n^2/Δ\})$. Every graph also admits $\widetilde{\mathcal O}(\min\{n^{4/3},N+(mn)^{3/5}\})$ rounds. Only $n,N$ are inputs; degrees, covers, and structural constants are used solely in the analysis. The unrestricted polynomial-identifier density extension remains open.

cs.DS · cs.CC · cs.DC

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37192

Tight Bounds for Randomized Generalized $k$-Server on Uniform Metrics

Junho Hwang

原文摘要

In the generalized $k$-server problem, each of $k$ servers moves in its own metric space, and a request $(r_1,\dots,r_k)$ is served once some server $i$ stands at the point $r_i$ of its space. We determine the randomized competitive ratio against an oblivious adversary when every space is a uniform metric. With unit distances the ratio is $Θ(k\log k)$: we give a $(k+1)\ln(2k)$-competitive algorithm and show that for large $k$ every algorithm has ratio at least $\frac{1}{20}k\ln k$, improving the bounds $O(k^2\log k)$ and $Ω(k)$ of Bienkowski, Jeż, and Schmidt. When server $i$ pays $w_i$ per move, the ratio is $\exp(Θ(k))$: we give a $20^k$-competitive algorithm, which also applies to weighted $k$-server on uniform metrics. This improves the $\exp(O(k^2))$ bound of Bijoy, Mondal, and Chiplunkar and matches the $Ω(2^k)$ lower bound of Ayyadevara and Chiplunkar up to the base of the exponent. Both algorithms follow normalized weights exactly, through couplings whose expected movement is controlled by the decrease of the logarithm of the total weight. The lower bound hides a random permutation among the solutions of random permutation constraints, which split into small, well-separated components, and then forbids one position to one server at a time.

cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37065

Polynomial-Time Solvability of the Mixed Evacuation Problem

Naoyuki Kamiyama

原文摘要

The mixed evacuation problem is a variant of the dynamic transshipment problem where there exist two modes of transportation and we allocate supplies to each mode of transportation in such a way that we can send all the supplies from sources to sinks within a given time limit. It is known that this problem can be solved in polynomial time when the number of sources and sinks is small. In this paper, we prove that the mixed evacuation problem can be solved in polynomial time with the ellipsoid method.

cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37018

Linear-Time FPT Rectilinear Planarity Testing of Series-Parallel Graphs

Giacomo Ortali

原文摘要

A planar graph is rectilinear planar if it admits a planar orthogonal drawing without bends. For series-parallel graphs in the variable embedding setting the best known testing algorithm takes $O(n^2)$ time. We show that rectilinear planarity of a series-parallel graph with maximum degree four can be tested in $2^{O(k)}\cdot n$ time, where $k$ is the number of degree-4 vertices; the planar embedding is not fixed. In particular, the running time is subquadratic when $k=o(\log n)$. Each node of the SPQ$^*$-tree stores the set of its admissible spiralities; we show that this set is a union of $2^{O(k)}$ arithmetic progressions of step two. All proofs are in the paper and are additionally verified in Lean 4 with Mathlib.

cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.32298

Exact Algorithms and Complexity of the Smallest Grammar Problem

Xiangle Chen

原文摘要

The Smallest Grammar Problem (SGP) asks for a smallest straight-line grammar generating a given string, with size measured by the total right-hand-side length. For an input of length $n\ge2$ over at most $σ$ symbols, where $2\leσ\le n$, let $R=\log_σn$. We give a deterministic exact algorithm running in $n^{O(1)}2^{O(n\log\log n/(R\sqrt{\log n}))}$ time and polynomial space, with constants independent of $σ$. This gives time $2^{O(n\log\log n/(\log n)^{3/2})}$ for fixed alphabets and $2^{O(n\log\log n/\sqrt{\log n})}$ for arbitrary alphabets, up to polynomial factors. The algorithm combines pairwise disjoint representative occurrences of dictionary strings, a sparse interval certificate, and the Boolean tensor contraction theorem of OpenAI. It explicitly enforces dictionary membership, rule boundaries, and the grammar-size budget. Independently of that contraction theorem, disjoint representatives yield exact algorithms in $O^*(1.872258^n)$ time and $2^{O((n/R)\log(R+1))}$ time using $O(n)$ words of space. Anchor-based grammar projections establish binary NP-completeness and reductions with tunable alphabet size. We state their consequences as unconditional quantitative transfers from SGP algorithms to sparse SAT algorithms, and quantify the additional loss from sparsifying general formulas.

cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37721

Local-to-Global Theorems Based on Cones with Applications to Graph Coloring

Anqi Li, Shayan Oveis Gharan

原文摘要

Local-to-Global theorems are a cornerstone of many of recent developments in theoretical computer science from coding theory and PCPs all the way to analyzing mixing time of Markov chains. Building on trickledown theorems on simplicial complexes, several techniques have been established to obtain tighter local-to-global theorems to analyze the spectral gap of the Glauber dynamics, namely matrix trickledown, ${\mathcal C}$-Lorentzian polynomials and more recently Bochner type inequalities. In this paper, we adopt non-local local-to-global/Bochner type inequalities on "cones", corresponding to the local neighborhood of a given vertex, to show that the Glauber dynamics mixes in polynomial time to sample proper colorings of maximum degree $Δ$ graphs as long as $q\geq 1.7408Δ$.

math.PR · cs.DM · cs.DS · math.CO

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2210.11132

A Search-Based Algorithm for Multistage Robust Discrete Linear Optimization and its Implementation

Michael Hartisch, Ulf Lorenz

原文摘要

Robust optimization models that allow decisions to adapt to newly revealed information remain computationally challenging and are often limited to two decision stages or are addressed heuristically or via approximation schemes. This challenge is further amplified when uncertainty sets depend on earlier decisions. Conventional approaches to such problems often require problem-specific reformulations and tailored algorithms, highlighting the need for an exact model-and-run approach. We address this gap by presenting an algorithmic framework for solving multistage robust discrete linear optimization problems. This exact approach adapts and integrates ideas from game-tree search, quantified conflict-driven clause learning, and integer linear programming to explore the minimax tree and is implemented in the open-source solver Yasol. The solver supports discrete decision variables across multiple stages, discrete uncertainty sets with polyhedral or decision-dependent structure, and mixed-integer recourse in the final stage. It can be used as a standalone executable or through a C++ library interface, allowing it to serve as a reference solver for exact methods in multistage robust discrete linear optimization. In an extensive computational study, we demonstrate the capabilities of our solver. The results show competitive performance against a reference approach from the literature for a protection-interdiction problem, as well as strong performance on bilevel benchmark instances. For a multistage cutting-stock problem, we demonstrate the substantial loss in solution quality that can arise from neglecting the multistage structure and show that our solver significantly outperforms decision-rule approximations in terms of computational efficiency while certifying the true multistage optimum.

math.OC · cs.DM · cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.30776

Report the tolerance, not the count: exact phylogenetic distance deconvolution with incomplete references

Haotian Tang

原文摘要

Phylogenetic distance deconvolution represents mixture-to-reference distances by weighted sources placed on a reference tree. We study the minimum number of strictly interior sources that explains a distance profile, and what incomplete references cost. On a positive-rational reduced tree we give an exact algorithm with 2^O(K) poly(B) bit complexity for a free positive mean pendant and any nonempty set of observed leaves; the single-exponential dependence on K is tight under ETH, already with every leaf observed. With arbitrary missing references and a prescribed pendant the problem is W[1]-hard in the source budget K, even on positive binary trees supplied with a strict explanation using at most K+1 sources. We then use the algorithm as an instrument. Removing references can only lower the minimum source count, never raise it, at every error tolerance. Which references are missing then matters far more than how many. Under nearest-to-source deletion a median of two references can be erased before the generating support stops being the unique smallest explanation, and that budget stays nearly flat as the panel grows (Spearman 0.10 over 20 to 361 references, against 0.82 for random loss). Discarding 7,931 of 10,575 references from a real 16S panel at random costs 1.8% of the tolerance at which one source suffices. Discarding comparably many as whole clades costs 90%. That tolerance needs neither ground truth nor an error model, which makes the model measurable on real data. The generating configuration's worst-leaf residual exceeds the one-source optimum in all 296 real ANI cases, and in 248 after refitting the common pendant. The phenomenon is not unobservable in practice. A point estimate of the count alone does not quantify it. Methods for this problem should report the tolerance at which an explanation of a given size exists.

q-bio.PE · cs.DS

查看论文
arXiv ↗PDF ↗
版本更新 · v4arXiv:2411.07030

Polynomial and Hyperplane Avoidance over the Integers with Applications to Integer-Point Counting

Grigorii Dakhno, Dmitry Gribanov, Nikita Kasianov, Anastasiia Kats, Andrey Kupavskii, Nikita Kuz'min, Stanislav Moiseev

原文摘要

We study the \emph{Polynomial Avoidance Problem}: given a finite collection $F \subseteq Z[x_1,\dots,x_n]$ of nonzero polynomials, find a vector $x \in Z^n$ of minimum $\ell_p$-norm such that $f(x)\neq0$ for every $f \in F$. Each polynomial is given sparsely as a list of its nonzero terms. The affine special case is the \emph{Hyperplane Avoidance Problem}. This special case arises in Barvinok-type algorithms for counting integer points in polyhedra, when certain rational generating functions must be evaluated at a removable singularity. Our main results are as follows: 1) Let $D:=\sum_{f\in F} \text{deg} f$. Every instance admits a feasible vector $x$ satisfying \[ \|x\|_1 \leq \min\left\{D,\frac{D+n}{2}\right\}. \] This bound is tight. Such a vector can be found by a deterministic algorithm whose bit complexity is polynomial in $D$ and the sparse encoding length of the input. Our proof uses a new algorithmic variant of the \emph{Combinatorial Nullstellensatz}; 2) In the affine case, with $m$ input polynomials, such a vector can be constructed by a fast deterministic polynomial-time algorithm using $O(nm)$ arithmetic operations. For the homogeneous case, Barvinok's original approach provides only the weaker guarantee $\|x\|_1 = O((nm)^{n-1})$; 3) The problem is NP-hard for every $p\in R_{\geq 1}\cup\{\infty\}$, even for homogeneous linear forms; 4) As an application, we improve the complexity bound for counting integer points in general rational polytopes. We also improve the bound for polyhedra of bounded codimension; this includes the counting version of the \emph{Unbounded Subset-Sum} problem as a special case.

cs.CC · cs.CG · cs.DM · cs.DS · math.CO

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36691

Differentially Private Preconditioned Power Iteration Method for Principal Component Analysis that Adapts to the Coherence

Duy V. Le, Ta Duy Nguyen, Alina Ene, Huy L. Nguyen

原文摘要

In Principal Component Analysis (PCA), we are given as input a matrix $A\in\mathbb{R}^{n\times d}$ and an integer $k\leq d$, and the goal is to find the top $k$ right-singular vectors of $A$. We consider the setting where each row of $A$ is the private data of an individual, and we design an $(ε,δ)$-differentially private algorithm whose utility guarantee improves with the coherence of the input matrix. Prior works were either restricted to the case $k=1$ or ensured significantly weaker privacy protections. Our algorithm is based on a preconditioned variant of the power iteration method that is designed to significantly reduce the noise needed to ensure privacy.

cs.DS

查看论文
arXiv ↗PDF ↗