Parallel algorithms for cographs and parity graphs with applications
Journal of Algorithms
Parallel recognition of complement reducible graphs and cotree construction
Discrete Applied Mathematics
An NC recognition algorithm for cographs
Journal of Parallel and Distributed Computing
Recognizing P4-sparse graphs in linear time
SIAM Journal on Computing
An introduction to parallel algorithms
An introduction to parallel algorithms
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
Parallel algorithm for cograph recognition with applications
Journal of Algorithms
A linear-time recognition algorithm for P4-reducible graphs
Theoretical Computer Science
Efficient parallel recognition algorithms of cographs and distance hereditary graphs
Discrete Applied Mathematics
Parallel computation: models and methods
Parallel computation: models and methods
A fast parallel algorithm to recognize P4-sparse graphs
Discrete Applied Mathematics
Graph classes: a survey
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
A time-optimal solution for the path cover problem on cographs
Theoretical Computer Science
An Optimal Parallel Co-Connectivity Algorithm
Theory of Computing Systems
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In this paper, we establish structural properties for the class of complement reducible graphs or cographs, which enable us to describe efficient parallel algorithms for recognizing cographs and for constructing the cotree of a graph if it is a cograph; if the input graph is not a cograph, both algorithms return an induced P4. For a graph on n vertices and m edges, both our cograph recognition and cotree construction algorithms run in O(log2 n) time and require O((n+m)/log n) processors on the EREW PRAM model of computation. Our algorithms are motivated by the work of Dahlhaus (Discrete Appl. Math. 57 (1995) 29-44) and take advantage of the optimal O(log n)-time computation of the co-connected components of a general graph (Theory Comput. Systems 37 (2004) 527-546) and of an optimal O(log n)-time parallel algorithm for computing the connected components of a cograph, which we present. Our results improve upon the previously known linear-processor parallel algorithms for the problems (Discrete Appl. Math. 57 (1995) 29-44; J. Algorithms 15 (1993) 284-313): we achieve a better time-processor product using a weaker model of computation and we provide a certificate (an induced P4) whenever our algorithms decide that the input graphs are not cographs.