Efficient parallel algorithms for chordal graphs

The author gives efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadth-first search tree and a depth-first search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism. The key to the results is an efficient parallel algorithm for finding a perfect elimination ordering.<<ETX>>

[1]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[2]  Fanica Gavril,et al.  Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph , 1972, SIAM J. Comput..

[3]  S. Sitharama Iyengar,et al.  NC Algorithms for Recognizing Chordal Graphs and k Trees , 1988, IEEE Trans. Computers.

[4]  Charles J. Colbourn,et al.  Linear Time Automorphism Algorithms for Trees, Interval Graphs, and Planar Graphs , 1981, SIAM J. Comput..

[5]  Robert E. Tarjan,et al.  Finding Biconnected Components and Computing Tree Functions in Logarithmic Parallel Time (Extended Summary) , 1984, FOCS.

[6]  Hillel Gazit,et al.  An optimal randomized parallel algorithm for finding connected components in a graph , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[7]  Kellogg S. Booth,et al.  Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms , 1976, J. Comput. Syst. Sci..

[8]  G. Dirac On rigid circuit graphs , 1961 .

[9]  Robert Schreiber,et al.  A New Implementation of Sparse Gaussian Elimination , 1982, TOMS.

[10]  Moni Naor,et al.  Fast parallel algorithms for chordal graphs , 1987, SIAM J. Comput..

[11]  John H. Reif,et al.  An optimal parallel algorithm for integer sorting , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[12]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[13]  Alok Aggarwal,et al.  A random NC algorithm for depth first search , 1987, Comb..

[14]  Gary L. Miller,et al.  Parallel tree contraction and its application , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[15]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[16]  Anders Edenbrandt,et al.  Chordal Graph Recognition is in NC , 1987, Inf. Process. Lett..

[17]  N. Klein Philip Efficient parallel algorithms for planar, chordal, and interval graph , 1988 .

[18]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[19]  Kellogg S. Booth,et al.  A Linear Time Algorithm for Deciding Interval Graph Isomorphism , 1979, JACM.

[20]  P. Gilmore,et al.  A Characterization of Comparability Graphs and of Interval Graphs , 1964, Canadian Journal of Mathematics.

[21]  Marek Karpinski,et al.  The Matching Problem for Strongly Chordal Graphs is in $NC$ , 1986 .

[22]  Philip N. Klein,et al.  An efficient parallel algorithm for planarity , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[23]  Anders Gunnar Edenbrandt Combinatorial Problems in Matrix Computation , 1985 .

[24]  D. R. Fulkerson,et al.  Incidence matrices and interval graphs , 1965 .

[25]  Vijay V. Vazirani,et al.  NC Algorithms for Comparability Graphs, Interval Gaphs, and Testing for Unique Perfect Matching , 1985, FSTTCS.

[26]  D. Rose Triangulated graphs and the elimination process , 1970 .

[27]  Richard Cole,et al.  Parallel merge sort , 1988, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[28]  John E. Savage,et al.  A Parallel Algorithm for Channel Routing , 1988, WG.

[29]  Claude Berge,et al.  Graphs and Hypergraphs , 2021, Clustering.

[30]  Uzi Vishkin,et al.  An O(log n) Parallel Connectivity Algorithm , 1982, J. Algorithms.