Showing papers on "Dominating set published in 1988"
TL;DR: Examples and properties of vertex domination-critical graphs are given, a method of constructing them is presented, and some open questions are posed.
Abstract: A dominating set in a graph G is a set of vertices D such that every vertex of G is either in D or is adjacent some vertex of D. The domination number Γ(G) of G is the minimum cardinality of any dominating set. A graph is vertex domination-critical if the removal of any vertex decreases its domination number. This paper gives examples and properties of vertex domination-critical graphs, presents a method of constructing them, and poses some open questions. In the process several results for arbitrary graphs are presented.
129 citations
TL;DR: Efficient algorithms for finding a minimum cardinality k-dominating set without taking power, connected k-Dominating set and total 1-domination set of a sun-free chordal graph are presented.
66 citations
TL;DR: An extension of this technique provides a method of studying the structure of directed graphs and directed social networks by partitioning the vertices of a graph using dominating vertices.
50 citations
TL;DR: This paper gives time algorithms for finding a minimum weighted total dominating set and aminimum weighted maximal irredundant set in a weighted interval graph, i.e., one that represents n intersecting intervals on the real line, each having a (possibly negative) real weight.
Abstract: In an undirected graph, a subset X of the nodes is a total dominating set if each node in the graph is a neighbor of some node in X. In contrast, X is an irredundant set if the closed neighborhood of each node in X is not contained in the union of closed neighborhoods of the other nodes in X. This paper gives $O( n\log n )$ and $O( n^4 )$ time algorithms for finding, respectively, a minimum weighted total dominating set and a minimum weighted maximal irredundant set in a weighted interval graph, i.e., one that represents n intersecting intervals on the real line, each having a (possibly negative) real weight.
45 citations
TL;DR: A linear time reduction of the problem of finding a minimum independent dominating set in a permutation graph, into that ofFinding a shortest maximal increasing subsequence, which improves on the O ( n 3 )-time algorithm given in [4].
34 citations
01 Jun 1988
TL;DR: A summary of systematic approach developed by the authors for spare allocation and reconfiguration is presented, modeled in graph-theoretic terms in which spare allocation for a specific reconfigurable system is shown to be equivalent to either a graph-matching or agraph-dominating-set problem.
Abstract: One approach to enhancing the yield of large area VLSI is through design for yield enhancement by means of restructurable interconnect, logic and computational elements. Although extensive literature exists concerning architectural design for inclusion of spares and restructuring mechanisms in memories and processor arrays, little research has been published on optimal spare allocation and reconfiguration in the presence of multiple defects. In this paper, a summary of a systematic approach developed by the authors for spare allocation and reconfiguration is presented. Spare allocation is modeled in graph theoretic terms in which spare allocation for a specific reconfigurable system is shown to be equivalent to either a graph matching or a graph dominating set problem. The complexity of optimal spare allocation for each of the problem classes is analyzed in this paper and reconfiguration algorithms are provided.
25 citations
TL;DR: The minimum number of edges required by such a graph is determined and similar results are given when the graph must remain connected upon any edge's removal and when the dominating set must remain fixed.
24 citations
TL;DR: This work presents an O(n2.5) time algorithm for finding the domatic number, as well as the desired partition, of an interval graph (which is a graph representing intersecting intervals on the real line), and gives an O-time algorithm for proper interval graphs (graphs for which no interval is properly contained within another).
23 citations