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Dynamic Algorithms for Submodular Matching

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

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ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Matching
  • Submodular
  • Dynamic
  • Polylogarithmic

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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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.ICALP.2025.19

Author Details

Kiarash Banihashem
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Leyla Biabani
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Samira Goudarzi
  • Department of Computer Science, University of Maryland, College Park, MD, USA
MohammadTaghi Hajiaghayi
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Peyman Jabbarzade
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Morteza Monemizadeh
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands

Funding

The work is partially supported by DARPA QuICC, ONR MURI 2024 award on Algorithms, Learning, and Game Theory, Army-Research Laboratory (ARL) grant W911NF2410052, NSF AF:Small grants 2218678, 2114269, 2347322.

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