Journal of Combinatorial Theory Series B
Distance-hereditary graphs, Steiner trees, and connected domination
SIAM Journal on Computing
A simple parallel tree contraction algorithm
Journal of Algorithms
Discrete Applied Mathematics - Computational combinatiorics
Polynomial time algorithms for Hamiltonian problems on bipartite distance-hereditary graphs
Information Processing Letters
Dominating Cliques in Distance-Hereditary Graphs
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
Characterization of Efficiently Solvable Problems on Distance-Hereditary Graphs
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Parallel Decomposition of Distance-Hereditary Graphs
ParNum '99 Proceedings of the 4th International ACPC Conference Including Special Tracks on Parallel Numerics and Parallel Computing in Image Processing, Video Processing, and Multimedia: Parallel Computation
On the Clique-Width of Perfect Graph Classes
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Dynamic Programming on Distance-Hereditary Graphs
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Journal of Parallel and Distributed Computing
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
An efficient parallel strategy for the perfect domination problem on distance-hereditary graphs
The Journal of Supercomputing
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
Discrete Applied Mathematics
A new approach to graph recognition and applications to distance-hereditary graphs
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Dynamic distance hereditary graphs using split decomposition
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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In this paper, we first present an O(|V| + |E|)-time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G = (V, E). This algorithm is faster than the previous best result which takes O(|V|2) time. Let Td(|V|, |E|) and Pd(|V|, |E|) denote the parallel time and processor complexities, respectively, required to construct a decomposition tree of a distance-hereditary graph on a PRAM model Md. We also show that this problem can be solved in O(Td(|V|, |E|) + log |V|) time using O(Pd(|V|, |E|) + (|V| + |E|)/ log |V|) processors on Md. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(log |V|) time using O((|V| + |E|)/ log |V|) processors on an EREW PRAM.