Discrete Mathematics - Graph colouring and variations
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
Parallel algorithms for cographs and parity graphs with applications
Journal of Algorithms
An NC recognition algorithm for cographs
Journal of Parallel and Distributed Computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Constant-time parallel recognition of split graphs
Information Processing Letters
Efficient parallel recognition algorithms of cographs and distance hereditary graphs
Discrete Applied Mathematics
A polynomial algorithm for the parity path problem on perfectly orientable graphs
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Parallel computation: models and methods
Parallel computation: models and methods
Even and odd pairs in comparability and in P4-comparability graphs
Discrete Applied Mathematics
Linear-time transitive orientation
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Concurrent threads and optimal parallel minimum spanning trees algorithm
Journal of the ACM (JACM)
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
Parallel Comparability Graph Recognition and Modular Decomposition
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Coloring permutation graphs in parallel
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
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We consider two problems pertaining to P4-comparability graphs, namely, the problem of recognizing whether a simple undirected graph is a P4-comparability graph and the problem of producing an acyclic P4-transitive orientation of such a graph. Sequential algorithms for these problems have been presented by Hoàng and Reed and very recently by Raschle and Simon, and by Nikolopoulos and Palios. In this paper, we establish properties of P4-comparability graphs which allow us to describe parallel algorithms for the recognition and orientation problems on this class of graphs; for a graph on n vertices and m edges, our algorithms run in O(log2n) time and require O(nm/log n) processors on the CREW PRAM model. Since the currently fastest sequential algorithms for these problems run in O(nm) time, our algorithms are cost-efficient; moreover, to the best of our knowledge, this is the first attempt to introduce parallelization in problems involving P4-comparability graphs. Our approach relies on the parallel computation and proper orientation, the P4-components of the input graph.