Efficient parallel algorithms on chordal graphs with a sparse tree representation

1994 ◽  
Author(s):  
Dahlhaus
Keyword(s):  
Parallel Algorithms ◽  
Chordal Graphs ◽  
Tree Representation

Parallel Algorithms for Recognizing P5-free and ${\bar P}_5$-free Weakly Chordal Graphs

2004 ◽  
Vol 14 (01) ◽  
pp. 119-129
Author(s):  
Stavros D. Nikolopoulos ◽  
Leonidas Palios
Keyword(s):  
Parallel Algorithms ◽  
Chordal Graphs ◽  
Input Graph ◽  
Model Of Computation ◽  
Erew Pram ◽  
Recognition Algorithms ◽  
Pram Model

We prove algorithmic characterizations of weakly chordal graphs, which lead to efficient parallel algorithms for recognizing P5-free and [Formula: see text]-free weakly chordal graphs. For an input graph on n vertices and m edges, our algorithms run in O( log 2n) time and require O(m2/ log n) processors on the EREW PRAM model of computation. The proposed recognition algorithms efficiently detect P5 s and [Formula: see text] in weakly chordal graphs in O( log n) time with O(m2/ log n) processors on the EREW PRAM. Additionally, we show how the algorithms can be augmented to provide a certificate for the existence of a P5 (or a [Formula: see text]) in case the input graph is not P5-free (respectively, [Formula: see text]-free) weakly chordal.

PARALLEL ALGORITHMS FOR HAMILTONIAN 2-SEPARATOR CHORDAL GRAPHS

2002 ◽  
Vol 12 (01) ◽  
pp. 51-64 ◽  
Author(s):  
B. S. PANDA ◽  
VIJAY NATARAJAN ◽  
SAJAL K. DAS
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Hamiltonian Cycle ◽  
Chordal Graph ◽  
Chordal Graphs ◽  
Pram Model ◽  
Crew Pram ◽  
Crcw Pram

In this paper we propose a parallel algorithm to construct a one-sided monotone polygon from a Hamiltonian 2-separator chordal graph. The algorithm requires O( log n) time and O(n) processors on the CREW PRAM model, where n is the number of vertices and m is the number of edges in the graph. We also propose parallel algorithms to recognize Hamiltonian 2-separator chordal graphs and to construct a Hamiltonian cycle in such a graph. They run in O( log 2 n) time using O(mn) processors on the CRCW PRAM model and O( log 2 n) time using O(m) processors on the CREW PRAM model, respectively.

Fast Parallel Algorithms for Chordal Graphs

1989 ◽  
Vol 18 (2) ◽  
pp. 327-349 ◽  
Author(s):  
Joseph Naor ◽  
Moni Naor ◽  
Alejandro A. Schäffer
Keyword(s):  
Parallel Algorithms ◽  
Chordal Graphs
Sign in / Sign up

Export Citation Format

Share Document