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Algorithms 2013, 6(1), 1-11; doi:10.3390/a6010001
Article

Maximum Disjoint Paths on Edge-Colored Graphs: Approximability and Tractability

1
, 2,*  and 1
1 Department of Computer Systems and Communication, University of Milan-Bicocca, Viale Sarca 336, Milan, Italy 2 Department of Humanities and Social Sciences, University of Bergamo, Via Donizzetti 3, Bergamo, Italy
* Author to whom correspondence should be addressed.
Received: 31 October 2012 / Revised: 13 December 2012 / Accepted: 18 December 2012 / Published: 27 December 2012
(This article belongs to the Special Issue Graph Algorithms)
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Abstract

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate the approximation and parameterized complexity of the problem. First, we show that, for any constant ε > 0, the problem is not approximable within factor c1-ε, where c is the number of colors, and that the corresponding decision problem is W[1]-hard when parametrized by the number of disjoint paths. Then, we present a fixed-parameter algorithm for the problem parameterized by the number and the length of the disjoint paths.
Keywords: social networks; disjoint paths; fixed-parameter algorithms; hardness of approximation social networks; disjoint paths; fixed-parameter algorithms; hardness of approximation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Bonizzoni, P.; Dondi, R.; Pirola, Y. Maximum Disjoint Paths on Edge-Colored Graphs: Approximability and Tractability. Algorithms 2013, 6, 1-11.

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