Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets. (22nd May 2013)

• Record Type: Journal Article
• Authors: Wang, Shiping; Zhu, Qingxin; Zhu, William; Min, Fan
• Other Names: Pomares Hector Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-05-22
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/519173
• Languages: English
• ISSNs: 1110-757X

Abstract

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.