2 Search Results for "Anand, Abhash"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.19
Dynamic Algorithms for Submodular Matching

Authors: Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The Maximum Submodular Matching (MSM) problem is a generalization of the classical Maximum Weight Matching (MWM) problem. In this problem, given a monotone submodular function f: 2^E → ℝ^{≥ 0} defined over subsets of edges of a graph G(V, E), we are asked to return a matching whose submodular value is maximum among all matchings in graph G(V, E). In this paper, we consider this problem in a fully dynamic setting against an oblivious adversary. In this setting, we are given a sequence 𝒮 of insertions and deletions of edges of the underlying graph G(V, E), along with an oracle access to the monotone submodular function f. The goal is to maintain a matching M such that, at any time t of sequence 𝒮, its submodular value is a good approximation of the value of the optimal submodular matching while keeping the number of operations minimal. We develop the first dynamic algorithm for the submodular matching problem, in which we maintain a matching whose submodular value is within expected (8 + ε)-approximation of the optimal submodular matching at any time t of sequence 𝒮 using expected amortized poly(log n, 1/(ε)) update time. Our approach incorporates a range of novel techniques, notably the concept of Uniform Hierarchical Caches (UHC) data structure along with its invariants, which lead to the first algorithm for fully dynamic submodular matching and may be of independent interest for designing dynamic algorithms for other problems.
Cite as

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh. Dynamic Algorithms for Submodular Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ICALP.2025.19,
  author =	{Banihashem, Kiarash and Biabani, Leyla and Goudarzi, Samira and Hajiaghayi, MohammadTaghi and Jabbarzade, Peyman and Monemizadeh, Morteza},
  title =	{{Dynamic Algorithms for Submodular Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.19},
  URN =		{urn:nbn:de:0030-drops-233969},
  doi =		{10.4230/LIPIcs.ICALP.2025.19},
  annote =	{Keywords: Matching, Submodular, Dynamic, Polylogarithmic}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.257
Maintaining Approximate Maximum Weighted Matching in Fully Dynamic Graphs

Authors: Abhash Anand, Surender Baswana, Manoj Gupta, and Sandeep Sen

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs. The algorithm maintains a matching M whose weight is at least 1/8 M^{*} where M^{*} is the weight of the maximum weight matching. The algorithm achieves an expected amortized O(log n log C) time per edge insertion or deletion, where C is the ratio of the weights of the highest weight edge to the smallest weight edge in the given graph.
Cite as

Abhash Anand, Surender Baswana, Manoj Gupta, and Sandeep Sen. Maintaining Approximate Maximum Weighted Matching in Fully Dynamic Graphs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 257-266, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

Copy BibTex To Clipboard

@InProceedings{anand_et_al:LIPIcs.FSTTCS.2012.257,
  author =	{Anand, Abhash and Baswana, Surender and Gupta, Manoj and Sen, Sandeep},
  title =	{{Maintaining Approximate Maximum Weighted Matching in Fully  Dynamic Graphs}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{257--266},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.257},
  URN =		{urn:nbn:de:0030-drops-38648},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.257},
  annote =	{Keywords: Matching, Dynamic Algorithm, Graph Algorithm}
}
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