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Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets

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  • Shiping Wang
  • Qingxin Zhu
  • William Zhu
  • Fan Min

Abstract

Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering. The main contributions of this paper are threefold. First, any graph is converted to a covering. Two graphs induce the same covering if and only if they are isomorphic. Second, some new concepts are defined in covering-based rough sets to correspond with ones in graph theory. The upper approximation number is essential to describe these concepts. Finally, from a new viewpoint of covering-based rough sets, the general reduct is defined, and its equivalent characterization for the edge cover is presented. These results show the potential for the connection between covering-based rough sets and graphs.

Suggested Citation

  • Shiping Wang & Qingxin Zhu & William Zhu & Fan Min, 2013. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    • Handle: RePEc:hin:jnljam:519173
    DOI: 10.1155/2013/519173
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    Cited by:

    1. Lihe Guan & Hong Wang, 2022. "A heuristic approximation algorithm of minimum dominating set based on rough set theory," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 752-769, August.

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