The K-Neighbor, R-Domination Problems On Interval-Graphs
Abbreviated Journal Title
Eur. J. Oper. Res.
COMPUTERS; FACILITIES; LOCATION; GRAPHS; NETWORKS; Management; Operations Research & Management Science
Many facility location problems are modeled as optimization problems on graphs. We consider the following facility location problem. Given a graph G = (V, E) with N vertices and M edges, the k-neighbor, r-dominating set ((k, r)-dominating set) problem is to determine the minimum cardinality set D subset-or-equal-to V such that, for every vertex u is-an-element-of V - D the distance between vertex u and at least k vertices in D is less than or equal to r. If we impose the condition that the graph induced by vertices in D should be connected, then the set D is a connected (k, r)-dominating set; if for each vertex in D there exists another vertex in D at a distance at most r, then the set D is a total(k, r)-dominating set; and if for each vertex in D there exists another vertex in D adjacent to it, then the set D is a reliable (k, r)-dominating set. In this paper, we present algorithms which run in O(k . N) time for solving the above problems on interval graphs, given its interval representation in sorted order. For the value of r = 1, our algorithms have a time-complexity of O(min(kN, M)).
European Journal of Operational Research
"The K-Neighbor, R-Domination Problems On Interval-Graphs" (1994). Faculty Bibliography 1990s. 1077.