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新论文 · v1arXiv:2611.17248

随机顺序流中的匹配：基于历史删除界

Matching in Random-Order Streams via Historical Deletion Bounds

Alireza Farhadi, Mohammadtaghi Hajiaghayi, Mohammad Mahdavi

AI 速读 基于摘要

针对固定图边以均匀随机顺序到达的场景，作者提出单遍流式最大匹配算法，在无权与加权图上均达到约0.713的近似比，核心工具是加权匹配的历史删除不等式。

cs.DS

arXiv ↗PDF ↗
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We study maximum matching when the edges of a fixed graph arrive in a uniformly random order. For any fixed $\varepsilon>0$, we give a one-pass algorithm that achieves, with high probability over the arrival order, approximation ratios of $0.71295$ for unweighted graphs and $0.71295-\varepsilon$ for weighted graphs, using near-linear space with an explicit charge for weight precision. Both approximation ratios hold for bipartite and general graphs. The algorithm does not require the stream length or the weight range in advance. The main structural ingredient is a historical deletion inequality for weighted matchings. The deletion price of a vertex set is the decrease in maximum matching weight when that set is removed. We bound the sum of these prices for pairwise disjoint vertex sets, even when each price is evaluated at a different stage as edges are added to the graph. Applied to the usual unfolding of integer weights, it transfers a bipartite cardinality certificate to an original weighted matching, even when the original graph is not bipartite. This transfer preserves the approximation coefficient. We combine this transfer with a refined analysis of fractional matchings in the two auxiliary graphs arising in the transfer theorem. An exact rational linear-programming certificate proves the stated constant for every feasible graph profile. The approximation guarantees and the new structural results are formally verified in Lean.

新论文 · v1arXiv:2611.15937

MOSAIC: Modular Obstacle and Spatial-Aware Framework for Manipulation In Cluttered Scenes

Richard Shi, Mohammad Mahdavian, Mehrdad Momeni Zadeh, Mohammed Elmahgiubi, Amir Rasouli

原文摘要

Vision-Language-Action (VLA) models have demonstrated strong performance in robotic manipulation, yet most rely primarily on 2D visual observations and language instructions, leaving scene geometry and obstacle relationships to be inferred implicitly. This limitation is particularly problematic in cluttered environments, where small spatial errors can lead to unintended contacts or collisions. We propose MOSAIC, a modular spatial- and obstacle-aware framework that can be integrated with pretrained VLA policies to improve object-level scene understanding and action generation. Our method augments the VLA backbone with an auxiliary semantic grounding task that predicts role-specific masks for the target object, destination region, and surrounding obstacles. We further combine the target and destination masks with depth estimated from 3D scene reconstruction to construct role-specific geometric tokens that are injected directly into the action expert. In addition, we propose obstacle-aware attention supervision that emphasizes obstacles near the robot body during task execution. The resulting attention features are subsequently injected into later action-expert layers to further guide action generation. Together, these components provide explicit semantic, geometric, and obstacle-aware cues while preserving the underlying pretrained VLA architecture. We evaluate our framework on pretrained VLA model using the RoboPRO benchmark, including visual perturbation tests, and further validate it on real-world manipulation tasks. MOSAIC improves the success rate by 5.1% in cluttered scenes, and by 9.7% under visual perturbations, with gains of up to 25.0% in the most challenging environment. We will release our code and dataset upon acceptance at the following Github page: https://mmahdavian.github.io/MOSAIC/

cs.RO · cs.CV

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04506

Dynamic Steiner Tree under Edge Updates

Jeff Giliberti, MohammadTaghi Hajiaghayi, Mohammad Mahdavi, Xinchen Yang

原文摘要

The Steiner tree problem is the canonical generalization of minimum spanning tree (MST). When connectivity is required only among a fixed subset of vertices (terminals), the goal is to maintain a minimum-cost tree connecting these terminals as the graph undergoes edge updates. While dynamic MST has been studied since the 1980s~[Frederickson, STOC'83, SICOMP'85], and the first sublinear-in-$n$ dynamic MST algorithm dates back almost thirty-five years to Eppstein, Galil, Italiano, and Nissenzweig~[FOCS'92, JACM'97], achieving sublinear-in-$n$ update time for dynamic Steiner tree has long remained open, as a single edge update can invalidate many routes in the underlying terminal metric closure. We present the first fully dynamic algorithm for Steiner tree that achieves a constant-factor approximation with sublinear-in-$n$ update time. For any fixed $0<ζ<1/2$, our deterministic algorithm maintains an $O_ζ(1)$-approximate Steiner tree for undirected graphs with polynomially bounded edge weights in $\widetilde O(n^{1/2+ζ})$ amortized update time, answering cost queries in $O(1)$ time, and reporting an explicit tree in $\widetilde O(n^{1+ζ})$ time. Our approach combines periodic terminal-metric rebuilds on a dynamic spanner with a top-tree dynamic program that localizes edge deletions and reconnects surviving components through a dynamic distance sparsifier. Along the way, we give a simpler randomized insertion-only algorithm with a better, explicit approximation ratio.

cs.DS

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arXiv ↗PDF ↗