Mathematics in Computer Science

, Volume 1, Issue 4, pp 673–688

Efficient Algorithms for Variants of Weighted Matching and Assignment Problems

Authors

  • Satyajit Banerjee
    • Honeywell Technology Solutions
    • Honeywell Technology Solutions
  • Subhas Kumar Ghosh
    • Honeywell Technology Solutions
Article

DOI: 10.1007/s11786-007-0028-0

Cite this article as:
Banerjee, S., Chowdhury, A.D. & Ghosh, S.K. Math.comput.sci. (2008) 1: 673. doi:10.1007/s11786-007-0028-0

Abstract.

Obtaining a matching in a graph satisfying a certain objective is an important class of graph problems. Matching algorithms have received attention for several decades. However, while there are efficient algorithms to obtain a maximum weight matching, not much is known about the maximum weight maximum cardinality, and maximum cardinality maximum weight matching problems for general graphs. Our contribution in this work is to show that for bounded weight input graphs one can obtain an algorithm for both maximum weight maximum cardinality (for real weights), and maximum cardinality maximum weight matching (for integer weights) by modifying the input and running the existing maximum weight matching algorithm. Also, given the current state of the art in maximum weight matching algorithms, we show that, for bounded weight input graphs, both maximum weight maximum cardinality, and maximum cardinality maximum weight matching have algorithms of similar complexities to that of maximum weight matching. Subsequently, we also obtain approximation algorithms for maximum weight maximum cardinality, and maximum cardinality maximum weight matching.

Mathematics Subject Classification (2000).

Primary 68R10, 68W25Secondary 05C85

Keywords.

Maximum weight maximum cardinality matchingapproximation algorithmgraph algorithmreduction

Copyright information

© Springer-Verlag 2008