New algorithms for maximum weight matching and a decomposition theorem
Artikel i vetenskaplig tidskrift, 2017

We revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights. We present an algorithm that operates by decomposing the problem into W unweighted versions of the problem, where W is the largest edge weight. Our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when W is small. One of the highlights of our algorithm is that it also produces an integral optimal dual solution; thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed. Our algorithm yields a new proof to the total dual integrality of Edmonds' matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs. We also consider the maximum weight capacitated b-matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed into W unweighted versions of the problem, where W is the largest edge weight. Our second algorithm is competitive with known algorithms when W is small. © 2016 INFORMS.

Maximum weight matching

Total dual integrality

Exact algorithms

Författare

Chien-Chung Huang

Chalmers, Data- och informationsteknik, Datavetenskap

T. Kavitha

Tata Institute of Fundamental Research

Mathematics of Operations Research

0364-765X (ISSN) 1526-5471 (eISSN)

Vol. 42 411-426

Ämneskategorier

Matematik

Styrkeområden

Building Futures

Fundament

Grundläggande vetenskaper

DOI

10.1287/moor.2016.0806