An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining

Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large graphs. Experimental evaluation is presented for multiple types of problem instances. These instances include unit disk graphs, which represent a model of wireless networks, random scale-free networks, as well as samples from two social networks and real-world graphs studied in network science. Our experiments indicate that RLS$_o$ performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search. The order-based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices. In addition, we propose a multi-start variant of RLS$_o$ that is suitable for solving the minimum weight dominating set problem. The application of RLS$_o$ in graph mining is also briefly demonstrated

Randomized Algorithms for Approximating a Connected Dominating Set in Wireless Sensor Networks

A Connected Dominating Set (CDS) of a graph representing a Wireless Sensor Network can be used as a virtual backbone for routing through the network. Since the sensors in the network are constrained by limited battery life, we desire a minimal CDS for the network, a known NP-hard problem. In this paper we present three randomized algorithms for constructing a CDS. We evaluate our algorithms using simulations and compare them to the two-hop K2 algorithm and two other greedy algorithms from the literature. After pruning, the randomized algorithms construct a CDS that are generally equivalent in size to those constructed by K2 while being asymptotically better in time and message complexity. This shows the potential of significant energy savings in using a randomized approach as a result of the reduced complexity

"Distributed routing schemes for ad hoc networks using d-SPR sets"

Michael Q. Rieck is an associate professor at Drake University in Des Moines, Iowa, USA. He holds a Ph. D. in mathematics from the University of South Florida. His primary research interests are in the areas of camera tracking and ad hoc wireless networks. He has also published results in the areas of triangle geometry, discrete mathematics, linear algebra, finite fields and association schemes.In this paper, we propose several new distributed algorithms for producing sets of nodes that can be used to form backbones of an ad hoc wireless network. Our focus is on producing small sets that are d-hop connected and d-dominating and have a desirable ‘d-shortest path property’ which we call d-SPR sets. These algorithms produce sets that are considerably smaller than those produced by an algorithm previously introduced by the authors. Our proposed algorithms, except the greedy ones, have constant time complexity in the restricted sense that the time required is unaffected by the size of the network, assuming however that the node degrees are bounded by a constant. The performance of the new algorithms are compared, and also compared with the authors' earlier algorithm, and with an adaptation of an algorithm of Wu and Li

A Distributed Greedy Algorithm for Constructing Connected Dominating Sets in Wireless Sensor Networks

A Connected Dominating Set (CDS) of the graph representing a Wireless Sensor Network can be used as a virtual backbone for routing in the network. Since sensor nodes are constrained by limited on-board batteries, it is desirable to have a small CDS for the network. However, constructing a minimum size CDS has been shown to be a NP-hard problem. In this paper we present a distributed greedy algorithm for constructing a CDS that we call Greedy Connect. Our algorithm operates in two phases, first constructing a dominating set and then connecting the nodes in this set. We evaluate our algorithm using simulations and compare it to the two-hop K2 algorithm in the literature. Depending on the network topology, our algorithm generally constructs a CDS that is up to 30% smaller in size than K

Construction of Pipelined Strategic Connected Dominating Set for Mobile Ad Hoc Networks

Efficient routing between nodes is the most important challenge in a Mobile Ad Hoc Network (MANET). A Connected Dominating Set (CDS) acts as a virtual backbone for routing in a MANET. Hence, the construction of CDS based on the need and its application plays a vital role in the applications of MANET. The PipeLined Strategic CDS (PLS-CDS) is constructed based on strategy, dynamic diameter and transmission range. The strategy used for selecting the starting node is, any source node in the network, which has its entire destination within a virtual pipelined coverage, instead of the node with maximum connectivity. The other nodes are then selected based on density and velocity. The proposed CDS also utilizes the energy of the nodes in the network in an optimized manner. Simulation results showed that the proposed algorithm is better in terms of size of the CDS and average hop per path length