Parallel recognition algorithms for chordal_planar graphs and planar k-trees

Authors:
B. S. Panda;Sajal K. Das
Affiliations:
Computer Science and Application Group, Department of Mathematics, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, 110 016, India;Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA
Venue:
Journal of Parallel and Distributed Computing
Year:
2005

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Abstract

This paper presents parallel algorithms for recognizing chordal_planar graphs and planar k-trees. Both the algorithms run in O(log^2n) time using O(n+m) processors on a concurrent-read and concurrent-write (CRCW), parallel random access machine (PRAM) model, where n and m are, respectively, the number of nodes and edges in the graph.The novelty of our chordal_planar graph recognition algorithm lies in that it is based on an elegant structural characterization of chordal_planar graphs proposed in this paper. Moreover, it is simpler than separately testing chordality and planarity. Our planar k-trees recognition algorithm is based on a new characterization of k-trees presented in this paper.