An optimal algorithm for the k-fixed-endpoint path cover on proper interval graphs
نویسندگان
چکیده
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 proper interval graph G and a particular set T of k vertices, the goal is to compute a path cover of G with minimum cardinality, such that the vertices of T are endpoints of these paths. 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 of proper interval graphs.
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