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
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
An introduction to parallel algorithms
An introduction to parallel algorithms
Polynomial time algorithms for Hamiltonian problems on bipartite distance-hereditary graphs
Information Processing Letters
Efficient parallel recognition algorithms of cographs and distance hereditary graphs
Discrete Applied Mathematics
Weighted connected domination and Steiner trees in distance-hereditary graphs
Discrete Applied Mathematics
Weighted connected k-domination and weighted k-dominating clique in distance-hereditary graphs
Theoretical Computer Science
Characterization of Efficiently Parallel Solvable Problems on Distance-Hereditary Graphs
SIAM Journal on Discrete Mathematics
Dominating Cliques in Distance-Hereditary Graphs
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
Dynamic Programming on Distance-Hereditary Graphs
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
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
Graphs and Hypergraphs
Finding a minimum path cover of a distance-hereditary graph in polynomial time
Discrete Applied Mathematics
Laminar structure of ptolemaic graphs with applications
Discrete Applied Mathematics
Longest Path Problems on Ptolemaic Graphs
IEICE - Transactions on Information and Systems
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In this paper, we first present an O(n + m)-time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G, where n and m are the number of vertices and edges of G, respectively. This algorithm is faster than the previous best known algorithm for the problem which takes O(n2) time. We also give an efficient parallel implementation of our sequential algorithm. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(log n) time using O((n + m)/log n) processors on an EREW PRAM.