Mertzios, G.B. and Unger, W. (2010) 'An optimal algorithm for the k-fixed-endpoint path cover on proper interval graphs.', *Mathematics in computer science.*, 3 (1). pp. 85-96.

## Abstract

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-fixed-endpoint path cover of G with respect to T is a set of vertex-disjoint simple 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.

Item Type: | Article |
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Additional Information: | Issue title: 'Advances in combinatorial algorithms I'. |

Keywords: | Proper interval graph, Perfect graph, Path cover, SNIR matrix, Linear-time algorithm. |

Full text: | PDF - Accepted Version (224Kb) |

Status: | Peer-reviewed |

Publisher Web site: | http://dx.doi.org/10.1007/s11786-009-0004-y |

Publisher statement: | The final publication is available at Springer via http://dx.doi.org/10.1007/s11786-009-0004-y. |

Record Created: | 16 Dec 2011 12:35 |

Last Modified: | 08 Sep 2014 10:44 |

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