A simple parallel tree contraction algorithm
Journal of Algorithms
An introduction to parallel algorithms
An introduction to parallel algorithms
On extendedP4-reducible and extendedP4-sparse graphs
Theoretical Computer Science
A fast parallel algorithm to recognize P4-sparse graphs
Discrete Applied Mathematics
An efficient parallel algorithm for maximum matching for some classes of graphs
Journal of Parallel and Distributed Computing
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Efficient Parallel Modular Decomposition (Extended Abstract)
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
A time-optimal solution for the path cover problem on cographs
Theoretical Computer Science
Parallel algorithms for Hamiltonian problems on quasi-threshold graphs
Journal of Parallel and Distributed Computing
The 2-Terminal-Set Path Cover Problem and Its Polynomial Solution on Cographs
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Cograph editing: complexity and parameterized algorithms
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Hi-index | 0.00 |
Nakano et al. [A time-optimal solution for the path cover problem on cographs, Theoret. Comput. Science 290 (2003) 1541-1556] presented a time- and work-optimal algorithm for finding the smallest number of vertex-disjoint paths that cover the vertices of a cograph and left open the problem of applying their technique into other classes of graphs. Motivated by this issue we generalize their technique and apply it to the class of P"4-sparse graphs, which forms a proper superclass of cographs. We show that the path cover problem on P"4-sparse graphs can also be optimally solved. More precisely, given a P"4-sparse graph G on n vertices and its modular decomposition tree, we describe an optimal parallel algorithm which returns a minimum path cover of G in O(logn) time using O(n/logn) processors on the EREW PRAM model. Our results generalize previous results and extend the family of perfect graphs admitting optimal solutions for the path cover problem.