An improved algorithm for the red-blue hitting set problem with the consecutive ones property

Authors:
Maw-Shang Chang;Hsiao-Han Chung;Chuang-Chieh Lin
Affiliations:
Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, Taiwan
Venue:
Information Processing Letters
Year:
2010

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Abstract

Let S be a set of elements. We say that a collection C of subsets of S has the consecutive ones property if there exist a linear order on S and a 0-1 matrix M, where M"i"j=1 if and only if the jth element is in the ith set in C, such that all 1's appear consecutively in each row of M. A set X@?C is hit by a subset S^'@?S if X@?S^'@A. Let C"r (red collection) and C"b (blue collection) be two collections of subsets of S respectively. The red-blue hitting set problem asks for a subset S^'@?S such that all sets in the blue collection are hit by S^', while the number of sets in the red collection hit by S^' has to be minimum. We present a shortest-path based algorithm with time complexity O(|C"b||S|+|C"r||S|+|S|^2) for this problem with C"r@?C"b having the consecutive ones property, which improves the previous time bound O(|C"r||C"b||S|^2) by Dom et al. (2008) [8].