Journal ArticleDOI
A unified approach to domination problems on interval graphs
TLDR
Une propriete tres simple des graphes intervalle is utilisee dans la realisation d'algorithmes a temps lineaire, developpes pour la resolution de differents problemes de domination as mentioned in this paper.About:
This article is published in Information Processing Letters.The article was published on 1988-04-28. It has received 130 citations till now. The article focuses on the topics: Interval (graph theory).read more
Citations
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Journal ArticleDOI
Divide-and-conquer approximation algorithms via spreading metrics
TL;DR: A polynomial time approximation algorithm is presented for problems modeled by the divide-and-conquer paradigm, such that all subgraphs for which the optimization problem is nontrivial have large diameters.
Journal ArticleDOI
Extremal Problems for Roman Domination
TL;DR: It is proved that $\gamma_R(G))\leq8n/11$ when $\delta(G)\geq2$ and $n\geq9$, and this is sharp.
Journal ArticleDOI
Bibliography on domination in graphs and some basic definitions of domination parameters
TL;DR: The following bibliography on Domination in Graphs has been compiled over the past six years at Clemson University, where it is expected that this bibliography will continue to grow at a steady rate.
Proceedings ArticleDOI
Selecting forwarding neighbors in wireless Ad Hoc networks
TL;DR: This paper proposes two practical heuristics for selecting the minimum number of forwarding neighbors: an &Ogr;(n log n) time algorithm that selects at most 6 times more forwarding neighbors than the optimum, and an improved approximation ratio of 3, where n is the number of 1- and 2-hop neighbors.
Journal ArticleDOI
Selecting forwarding neighbors in wireless ad hoc networks
TL;DR: This paper proposes two practical heuristics for selecting the minimum number of forwarding neighbors: an O(nlog n) time algorithm that selects at most 6 times more forwarding neighbors than the optimum, and an improved approximation ratio of 3, where n is the number of 1- and 2-hop neighbors.
References
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Journal ArticleDOI
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
TL;DR: The consecutive ones test for the consecutive ones property in matrices and for graph planarity is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.
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Domination, independent domination, and duality in strongly chordal graphs☆
TL;DR: Polynomial algorithms to locate minimum weight dominating sets and independent dominating sets in strongly chordal graphs and to efficiently solve certain optimization problems for totally balanced matrices are presented.
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Dominating Sets in Chordal Graphs
TL;DR: It is shown that the problem of finding a minimum dominating set in a chordal graph is NP-complete, even when restricted to undirected path graphs, but exhibit a linear time greedy algorithm for the problem further restricted to directed path graphs.
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Steiner trees, connected domination and strongly chordal graphs
TL;DR: A polynomial algorithm and a min-max theorem for the cardinality Steiner problem in strongly chordal graphs and a polynometric algorithm for the weighted connected dominating set problem in series-parallel graphs are given.
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On the Algorithmic Complexity of Total Domination
TL;DR: For undirected path graphs, the problem remains NP-complete as discussed by the authors, and it was shown that the problem is not solvable in linear time for any tree, even in the case of trees.