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2010

An Optimal Algorithm for the k-Fixed-Endpoint Path Cover on Proper Interval Graphs

7 years 11 months ago
An Optimal Algorithm for the k-Fixed-Endpoint Path Cover on Proper Interval Graphs
In this paper we consider the k-fixed-endpoint path cover problem on proper interval graphs, which is a generalization of the path cover problem. Given a graph G and a set T of k vertices, a k-fixedendpoint path cover of G with respect to T is a set of vertex-disjoint paths that covers the vertices of G, such that the vertices of T are all endpoints of these paths. The goal is to compute a k-fixed-endpoint path cover of G with minimum cardinality. We propose an optimal algorithm for this problem with runtime O(n), where n is the number of intervals in G. This algorithm is based on the Stair Normal Interval Representation (SNIR) matrix that characterizes proper interval graphs. In this characterization, every maximal clique of the graph is represented by one matrix element; the proposed algorithm uses this structural property, in order to determine directly the paths in an optimal solution.
George B. Mertzios, Walter Unger
Added 20 May 2011
Updated 20 May 2011
Type Journal
Year 2010
Where MICS
Authors George B. Mertzios, Walter Unger
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