Approximation Algorithms for Permanent Dominating Set Problem on Dynamic Networks

Abstract

A temporal graph is a graph whose node and/or edge set changes with time. Many dynamic networks in practice can be modeled as temporal graphs with different properties. Finding different types of dominating sets in such graphs is an important problem for efficient routing, broadcasting, or information dissemination in the network. In this paper, we address the problems of finding the minimum permanent dominating set and maximum k-dominant node set in temporal graphs modeled as evolving graphs. The problems are first shown to be NP-hard. A \(\ln (n\tau )\)-approximation algorithm is then presented for finding a minimum permanent dominating set, where n is the number of nodes, and \(\tau \) is the lifetime of the given temporal graph. Detailed simulation results on some real life data sets representing different networks are also presented to evaluate the performance of the proposed algorithm. Finally, a \((1-\frac{1}{e})\)-approximation algorithm is presented for finding a maximum k-dominant node set.