On Maximal Chain Subgraphs and Covers of Bipartite Graphs
In this paper, we address three related problems. One is the enumeration of all the maximal edge induced chain subgraphs of a bipartite graph, for which we provide a polynomial delay algorithm. We give bounds on the number of maximal chain subgraphs for a bipartite graph and use them to establish the input-sensitive complexity of the enumeration problem. The second problem we treat is the one of finding the minimum number of chain subgraphs needed to cover all the edges a bipartite graph. For this we provide an exact exponential algorithm with a non trivial complexity. Finally, we approach the problem of enumerating all minimal chain subgraph covers of a bipartite graph and show that it can be solved in quasi-polynomial time.
KeywordsChain subgraph cover problem Enumeration algorithms Exact exponential algorithms
T. Calamoneri is supported in part by the Italian Ministry of Education, University, and Research (MIUR) under PRIN 2012C4E3KT national research project “AMANDA - Algorithmics for MAssive and Networked DAta” and in part by Sapienza University of Rome project “Graph Algorithms for Phylogenetics: A Promising Approach”. M. Gastaldello is supported by the Università Italo-Francese project “Algorithms and Models for the solution of difficult problems in biology”. A. Mary is supported by the ANR project GraphEN “Enumération dans les graphes et les hypergraphes: algorithmes et complexité”, ANR-15-CE40-0009.
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