Name
Abstract | ||
|---|---|---|
Suppose G=(V,E) is a simple graph and k is a fixed positive integer. A subset D@?V is a distancek-dominating set of G if for every u@?V, there exists a vertex v@?D such that d"G(u,v)@?k, where d"G(u,v) is the distance between u and v in G. A set D@?V is a distancek-paired-dominating set of G if D is a distance k-dominating set and the induced subgraph G[D] contains a perfect matching. Given a graph G=(V,E) and a fixed integer k0, the Min Distancek-Paired-Dom Set problem is to find a minimum cardinality distance k-paired-dominating set of G. In this paper, we show that the decision version of Min Distancek-Paired-Dom Set is NP-complete for undirected path graphs. This strengthens the complexity of decision version of Min Distancek-Paired-Dom Set problem in chordal graphs. We show that for a given graph G, unless NP@?DTIME(n^O^(^l^o^g^l^o^g^n^)), Min Distancek-Paired-Dom Set problem cannot be approximated within a factor of (1-@e)lnn for any @e0, where n is the number of vertices in G. We also show that Min Distancek-Paired-Dom Set problem is APX-complete for graphs with degree bounded by 3. On the positive side, we present a linear time algorithm to compute the minimum cardinality of a distance k-paired-dominating set of a strongly chordal graph G if a strong elimination ordering of G is provided. We show that for a given graph G, Min Distancek-Paired-Dom Set problem can be approximated with an approximation factor of 1+ln2+k@?ln(@D(G)), where @D(G) denotes the maximum degree of G. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.tcs.2012.08.024 | Theor. Comput. Sci. |
Keywords | DocType | Volume |
undirected path graph,Min Distancek-Paired-Dom Set problem,simple graph,graph G,decision version,distance paired-domination problem,Min Distancek-Paired-Dom Set,chordal graph,G. A,distancek-paired-dominating set,distancek-dominating set | Journal | 459, |
ISSN | Citations | PageRank |
0304-3975 | 4 | 0.44 |
References | Authors | |
23 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gerard J. Chang | 1 | 1163 | 112.81 |
| B. S. Panda | 2 | 99 | 21.18 |
| D. Pradhan | 3 | 21 | 2.52 |