Parallel recognition and location algorithms for chordal graphs using distance matrices

  • Stavros D. Nikolopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 854)


We present efficient parallel algorithms for recognizing chordal graphs and locating all maximal cliques of a chordal graph G=(V,E). Our techniques are based on partitioning the vertex set V using information contained in the distance matrix of the graph. We use these properties to formulate parallel algorithms which, given a graph G=(V,E) and its adjacency-level sets, decide whether or not G is a chordal graph, and, if so, locate all maximal cliques of the graph in time O(k) by using δ2·n2/k processors on a CRCW-PRAM, where δ is the maximum degree of a vertex in G and 1≤k≤n. The construction of the adjacency-level sets can be done by computing first the distance matrix of the graph, in time O(logn) with O(nβ+DG) processors, where DG is the output size of the partitions and β=2.376, and then extracting all necessary set information. Hence, the overall time and processor complexity of both algorithms are O(logn) and O(max{δ2·n2/logn, nβ+DG}), respectively. These results imply that, for δ≤√nlogn, the proposed algorithms improve in performance upon the best-known algorithms for these problems.


Parallel algorithms Chordal graphs Recognition Maximal cliques Distance matrix Graph partition Complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Stavros D. Nikolopoulos
    • 1
  1. 1.Department of Computer ScienceUniversity of CyprusNicosiaCyprus

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