Dominating set

About: Dominating set is a research topic. Over the lifetime, 4058 publications have been published within this topic receiving 72432 citations. The topic is also known as: dominating set problem.

A Dominating-Set-Based Routing Scheme in Ad Hoc Wireless Networks

Abstract: 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 a promising approach, where the searching space for a route is reduced to nodes in the set. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. In this paper, we propose a simple and efficient distributed algorithm for calculating connected dominating set in ad hoc wireless networks, where connections of nodes are determined by their geographical distances. We also propose an update/recalculation algorithm for the connected dominating set when the topology of the ad hoc wireless network changes dynamically. Our simulation results show that the proposed approach outperforms a classical algorithm in terms of finding a small connected dominating set and doing so quickly. Our approach can be potentially used in designing efficient routing algorithms based on a connected dominating set.

A Polynomial-Time Approximation Scheme for the Minimum-Connected Dominating Set in Ad Hoc Wireless Networks

Abstract: A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. A minimum-connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum-connected dominating set in unit-disk graphs. In this paper, we design a (1 + 1/s)-approximation for the minimum-connected dominating set in unit-disk graphs, running in time nO((s log s)2). © 2003 Wiley Periodicals, Inc.

What cannot be computed locally

Abstract: We give time lower bounds for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS). In k communication rounds, MVC and MDS can only be approximated by factors Ω(nc/k2/k) and Ω(Δ>1/k/k) for some constant c, where n and Δ denote the number of nodes and the largest degree in the graph. The number of rounds required in order to achieve a constant or even only a polylogarithmic approximation ratio is at least Ω(√log n/log log n) and Ω(logΔ/ log log Δ). By a simple reduction, the latter lower bounds also hold for the construction of maximal matchings and maximal independent sets.

Domination in Graphs Applied to Electric Power Networks

Abstract: The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graphs. We consider the graph theoretical representation of this problem as a variation of the dominating set problem and define a set S to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph G is the power domination number $\gamma_P(G)$. We show that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs. On the other hand, we give a linear algorithm to solve the PDS for trees. In addition, we investigate theoretical properties of $\gamma_P(T)$ in trees T.