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Semi-Streaming Algorithms for Weighted k-Disjoint Matchings

Authors S M Ferdous , Bhargav Samineni , Alex Pothen , Mahantesh Halappanavar , Bala Krishnamoorthy

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Author Details

S M Ferdous
  • Pacific Northwest National Laboratory, Richland, WA, USA
Bhargav Samineni
  • The University of Texas at Austin, TX, USA
Alex Pothen
  • Purdue University, West Lafayette, IN, USA
Mahantesh Halappanavar
  • Pacific Northwest National Laboratory, Richland, WA, USA
Bala Krishnamoorthy
  • Washington State University Vancouver, WA, USA

Funding

  • Ferdous, S M: Laboratory Directed Research and Development Program at PNNL.
  • Samineni, Bhargav: U.S. DOE Science Undergraduate Laboratory Internships (SULI) program.
  • Pothen, Alex: U.S. Department of Energy SC-0022260.
  • Halappanavar, Mahantesh: U.S. Department of Energy 17-SC-20-SC (ECP ExaGraph) at PNNL.

Cite AsGet BibTex

S M Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy. Semi-Streaming Algorithms for Weighted k-Disjoint Matchings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 53:1-53:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.53

Abstract

We design and implement two single-pass semi-streaming algorithms for the maximum weight k-disjoint matching (k-DM) problem. Given an integer k, the k-DM problem is to find k pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For k ≥ 2, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is 1/(3+ε)-approximate. We also develop an approximation preserving reduction from k-DM to the maximum weight b-matching problem. Leveraging this reduction and an existing semi-streaming b-matching algorithm, we design a (1/(2+ε))(1 - 1/(k+1))-approximate semi-streaming algorithm for k-DM. For any constant ε > 0, both of these algorithms require O(nk log_{1+ε}² n) bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the k-DM problem. We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6× to 512× less) and were faster in runtime than the offline algorithms. Our solutions were often within 5% of the best weights from the offline algorithms. We highlight that the existing offline algorithms run out of 1 TB memory for most of the large instances (> 1 billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for k = 8.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Matchings and factors
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Matchings
  • Semi-Streaming Algorithms
  • Approximation Algorithms

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