Recognition of probe cographs and partitioned probe distance hereditary graphs

  • Authors:

  • David B. Chandler;Maw-Shang Chang;Ton Kloks;Jiping Liu;Sheng-Lung Peng

  • Affiliations:

  • Institute of Mathematics, Academia Sinica, Nangang, Taipei, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan;-;Department of Mathematics and Computer Science, The University of Lethbridge, Alberta, Canada;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan

  • Venue:
  • AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2006

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Abstract

Given a class of graphs ${\cal G}$, a graph G is a probe graph of ${\cal G}$ if its vertices can be partitioned into two sets ℙ (the probes) and ℕ (nonprobes), where ℕ is an independent set, such that G can be embedded into a graph of ${\cal G}$ by adding edges between certain vertices of ℕ. If the partition of the vertices into probes and nonprobes is part of the input, then we call the graph a partitioned probe graph of ${\cal G}$. We give the first polynomial-time algorithm for recognizing partitioned probe distance-hereditary graphs. By using a novel data structure for storing a multiset of sets of numbers, the running time of this algorithm is ${O}(\mathfrak\it{n}^2)$, where $\mathfrak\it{n}$ is the number of vertices of the input graph. We also show that the recognition of both partitioned and unpartitioned probe cographs can be done in ${O}(\mathfrak\it{n}^2)$ time.