Pointwise Lipschitz Continuous Graph Algorithms
Quanquan C. Liu, Grigoris Velegkas, Yuichi Yoshida, Felix Zhou

TL;DR
This paper introduces a linear programming-based approach to develop graph algorithms with provably optimal stability, improving robustness and recourse bounds for problems like minimum cut and b-matching.
Contribution
It presents the first LP-based minimum S-T cut algorithm with optimal Lipschitz constant and extends to dynamic settings with non-trivial recourse bounds, also improving b-matching algorithms.
Findings
LP-based minimum S-T cut with optimal Lipschitz constant
First dynamic minimum S-T cut algorithm with non-trivial recourse
Improved Lipschitz bounds for b-matching algorithms
Abstract
In many real-world applications, it is undesirable to drastically change the problem solution after a small perturbation in the input, as unstable outputs can lead to costly transaction fees, privacy and security concerns, reduced user trust, and lack of replicability. Despite the widespread application of graph algorithms, many classical algorithms are not robust to small input disturbances. Towards addressing this issue, we study the pointwise Lipschitz continuity of graph algorithms, a notion of stability introduced by Kumabe and Yoshida [KY23, FOCS'23] and further studied in related settings [KY24, ICALP'24], [KY25, SODA'25], [GKY25, ESA'25]. Our main result is a linear programming (LP) based minimum - cut algorithm with a provably optimal Lipschitz constant, as witnessed by an accompanying lower bound. As a direct corollary, we give the first dynamic minimum - cut…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Face and Expression Recognition · Advanced Optimization Algorithms Research
