Joshua Brakensiek, David Conlon, Venkatesan Guruswami, Xiaoyu He, Jiaxi Nie, Maya Sankar, Hung-Hsun Hans Yu
In the study of constraint satisfaction problems (CSPs), the non-redundancy of a relation measures the maximum number of clauses in a CSP instance which can be logically independent. In the last few years, CSP non-redundancy has found a number of applications including in query complexity, sparsification, kernelization and streaming. In this paper, we present a novel technique for upper-bounding the non-redundancy of some relations using locally decodable codes (LDCs) and locally correctable codes (LCCs). More precisely, known limitations on the structure of 2-query LDCs and LCCs can be translated into limitations on the size of certain non-redundant CSP instances. This technique builds on a technique used by Brakensiek and Guruswami [STOC 2025] to bound non-redundancy via techniques from matching vector codes. Using LDCs and LCCs, we give improved upper bounds on non-redundancy of the BCK predicate pioneered by Bessiere, Carbonnel, and Katsirelos [AAAI 2020] as well as its well-studied Boolean variant. We also give the first example of a Boolean predicate whose non-redundancy is provably not of the form $n^{k\pm o(1)}$ for some positive integer $k$.
Siyuan Yang, Junning Lyu, Xiaoyu He, Lakmal Seneviratne, Shaoming He
This paper studies UAV swarm search in GNSS-denied maritime environments, where inter-UAV ranging drives cooperative localization and uncertainty propagates along the multi-hop reference chain, affecting connectivity, collision avoidance, and search effectiveness. We propose an uncertainty-aware control barrier function (CBF) framework approximating cascading localization covariance through Fisher information matrices. First, the cascading covariance model captures how ranging noise and neighbor uncertainty accumulate along the localization chain. Second, uncertainty-tightened CBFs incorporate the covariance model and its rate into margins for connectivity maintenance and collision avoidance, with conditional invariance and graceful-degradation bounds. Third, a hierarchical Voronoi-target strategy with formation keeping supports efficient forward-looking coverage. The distributed controller is validated with a standard unbiased extended Kalman filter in the loop. The framework is demonstrated on several polygon shapes and swarm sizes from 6 to 30 sUAVs. An estimator-in-the-loop run completes the search in 302.5 s, 20 Monte Carlo deployments confirm repeatable completion with all local QPs feasible and containment in at least 98.97% of UAV-frames, and six MBZIRC runs provide estimator-in-the-loop evidence. The source code is publicly available.