A Parameterized View on Matroid Optimization Problems

  • Dániel Marx
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

Abstract

Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial O(n k ) time brute force algorithm for finding a k-element solution, we try to give algorithms with uniformly polynomial (i.e., f(k) Open image in new window n O(1)) running time. The main result is that if the ground set of a represented matroid is partitioned into blocks of size ℓ, then we can determine in f(k,ℓ) Open image in new window n O(1) randomized time whether there is an independent set that is the union of k blocks. As consequence, algorithms with similar running time are obtained for other problems such as finding a k-set in the intersection of ℓ matroids, or finding k terminals in a network such that each of them can be connected simultaneously to the source by ℓ disjoint paths.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dániel Marx
    • 1
  1. 1.Institut fürInformatikHumboldt-Universität zu BerlinBerlinGermany

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