Charbit, Pierre and Habib, Michel and Mamcarz, Antoine - Influence of the tie-break rule on the end-vertex problem

dmtcs:2081 - Discrete Mathematics & Theoretical Computer Science, July 29, 2014, Vol. 16 no. 2 (in progress)
Influence of the tie-break rule on the end-vertex problem

Authors: Charbit, Pierre and Habib, Michel and Mamcarz, Antoine

End-vertices of a given graph search may have some nice properties, as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial, see Rose, Tarjan and Lueker 1976. Therefore it is interesting to consider if these vertices can be recognized in polynomial time or not, as first studied in Corneil, Köhler and Lanlignel 2010. A graph search is a mechanism for systematically visiting the vertices of a graph. At each step of a graph search, the key point is the choice of the next vertex to be explored. Graph searches only differ by this selection mechanism during which a tie-break rule is used. In this paper we study how the choice of the tie-break in case of equality during the search, for a given graph search including the classic ones such as BFS and DFS, can determine the complexity of the end-vertex problem. In particular we prove a counterintuitive NP-completeness result for Breadth First Search solving a problem raised in Corneil, Köhler and Lanlignel 2010.


Source : oai:HAL:hal-01101514v1
Volume: Vol. 16 no. 2 (in progress)
Section: PRIMA 2013
Published on: July 29, 2014
Submitted on: November 1, 2013
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]


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