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A set S V is a dominating set of a graph G = (V; E) if each vertex in V is either in S or is adjacent to a vertex in S. A vertex is said to dominate itself and all its neighbors. ...
How well can the maximum size of an independent set, or the minimum size of a dominating set of a graph in which all degrees are at most d be approximated by a randomized constant...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
Efficient routing among a set of mobile hosts (also called nodes) is one of the most important functions in ad hoc wireless networks. Routing based on a connected dominating set is...
Dealing with the NP-complete Dominating Set problem on graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In parti...
Jochen Alber, Michael R. Fellows, Rolf Niedermeier
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G) is an m-tuple dominating set if S dominates every vertex of G at least m times, and an m-dominating...
A k-hop dominating set is a subset of nodes such that each node not in the set can be reached within k hops from at least one node in the set. A connected k-hop dominating set can ...
An ad hoc network is a multihop wireless communication network supporting mobile users. Network performance degradation is a major problem as the network becomes larger. Clusterin...
We provide self-stabilizing algorithms to obtain and maintain a maximal matching, maximal independent set or minimal dominating set in a given system graph. They converge in linea...
Wayne Goddard, Stephen T. Hedetniemi, David Pokras...
Let F1, F2, . . . , Fk be graphs with the same vertex set V . A subset S V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a fac...
Peter Dankelmann, Michael A. Henning, Wayne Goddar...