On Maximal Chain Subgraphs and Covers of Bipartite Graphs

  • Tiziana Calamoneri
  • Mattia Gastaldello
  • Arnaud Mary
  • Marie-France Sagot
  • Blerina Sinaimeri
Conference paper

DOI: 10.1007/978-3-319-44543-4_11

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)
Cite this paper as:
Calamoneri T., Gastaldello M., Mary A., Sagot MF., Sinaimeri B. (2016) On Maximal Chain Subgraphs and Covers of Bipartite Graphs. In: Mäkinen V., Puglisi S., Salmela L. (eds) Combinatorial Algorithms. IWOCA 2016. Lecture Notes in Computer Science, vol 9843. Springer, Cham

Abstract

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.

Keywords

Chain subgraph cover problem Enumeration algorithms Exact exponential algorithms 

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Tiziana Calamoneri
    • 1
  • Mattia Gastaldello
    • 1
    • 2
  • Arnaud Mary
    • 2
  • Marie-France Sagot
    • 2
  • Blerina Sinaimeri
    • 2
  1. 1.Sapienza University of RomeRomaItaly
  2. 2.INRIA and Université de Lyon, Université Lyon 1, LBBE, CNRS UMR558VilleurbanneFrance

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