DROPS

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.153

Dynamic Set Cover with Worst-Case Recourse

Authors: Shay Solomon and Amitai Uzrad

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

In the dynamic set cover (SC) problem, the input is a dynamic universe of at most n elements and a fixed collection of m sets, where each element belongs to at most f sets and each set has a cost in [1/C,1]. The objective is to efficiently maintain an approximate minimum SC under element updates. Efficiency is primarily measured by the update time, but another important parameter is the recourse (the number of changes to solution per update). Ideally, one would like to achieve low worst-case bounds on both update time and recourse. One can achieve an approximation of (1+ε)ln n (greedy-based) or (1+ε)f (primal–dual-based) with worst-case update time O(f log n) (ignoring ε-dependencies). However, despite a large body of work, no algorithm with low update time (even amortized) and nontrivial worst-case recourse is known even for unweighted instances (C = 1)! We remedy this by providing a transformation that, given a SC algorithm with approximation α and update time T as a black-box, returns a set cover algorithm with approximation (2 + ε)α, update time O(T + α C) and worst-case recourse O(α C). Our main results are obtained by leveraging this transformation for constant C: - For f = O(log n), applying the transformation on the best primal-dual-based algorithm yields worst-case recourse O(f). For constant f (e.g., vertex cover), we get near-optimal bounds on all parameters. - For f = Ω(log n), applying the transformation on the best greedy-based algorithm yields worst-case recourse O(log n). As our main technical contribution, we show that by opening the black box and exploiting a certain robustness property of the greedy-based algorithm, the worst-case recourse can be reduced to O(1), without sacrificing the other parameters, yielding a ((2 + ε) ln n)-approximation with worst-case update time O(flog n) and O(1) worst-case recourse.

Cite as

Shay Solomon and Amitai Uzrad. Dynamic Set Cover with Worst-Case Recourse. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 153:1-153:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{solomon_et_al:LIPIcs.ICALP.2026.153,
  author =	{Solomon, Shay and Uzrad, Amitai},
  title =	{{Dynamic Set Cover with Worst-Case Recourse}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{153:1--153:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.153},
  URN =		{urn:nbn:de:0030-drops-265425},
  doi =		{10.4230/LIPIcs.ICALP.2026.153},
  annote =	{Keywords: Dynamic graphs, set cover, recourse}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.26

Engineering Algorithms for Dynamic Greedy Set Cover

Authors: Amitai Uzrad

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks - such as [GKKP(STOC'17); SU(STOC'23); SUZ(FOCS'24)] - which we simplify by identifying and modifying intricate subroutines that optimize asymptotic bounds but hinder practical performance. We evaluate these algorithms based on solution quality (set cover size) and efficiency, which comprises update time - the time required to update the solution following each insertion/deletion - and recourse - the number of changes made to the solution per update. Each algorithm uses a parameter β to balance quality against efficiency; we investigate the influence of this tradeoff parameter on each algorithm and then perform a comparative analysis to evaluate the algorithms against each other. Our results provide the first practical insights into which algorithmic strategies provide the most value in realistic scenarios.

Cite as

Amitai Uzrad. Engineering Algorithms for Dynamic Greedy Set Cover. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{uzrad:LIPIcs.SEA.2026.26,
  author =	{Uzrad, Amitai},
  title =	{{Engineering Algorithms for Dynamic Greedy Set Cover}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.26},
  URN =		{urn:nbn:de:0030-drops-260308},
  doi =		{10.4230/LIPIcs.SEA.2026.26},
  annote =	{Keywords: Dynamic graphs, set cover, recourse}
}

Search Results

Documents authored by Uzrad, Amitai

Dynamic Set Cover with Worst-Case Recourse

Abstract

Cite as

Engineering Algorithms for Dynamic Greedy Set Cover

Abstract

Cite as

Thanks for your feedback!

Could not send message