The minimum broadcast range assignment problem on linear multi-hop wireless networks

Abstract

Given a set N of radio stations located on an Euclidean space, a source station s and an integer h (1 less than or equal to h less than or equal to N - 1), the minimum bounded-hop broadcast range assignment problem consists in finding a range assignment for N of minimum total power consumption that allows broadcast operations from s to every station in N in at most h hops. The problem is known to be NP-hard on d-dimensional spaces for any d greater than or equal to 2 (18th Annual Symp. on Theoretical Aspects of Computer Science (STACS'01), Lecture Notes in Computer Science, Vol. 1770, 2000, pp. 651-660.) and some efficient approximation algorithms have been given in Clementi et al. and Wann et al. (18th Annual Symp. on Theoretical Aspects of Computer Science (STACS'01), Lecture Notes in Computer Science, Vol. 1770, 2000, pp. 651-660, IEEE INFOCOM'01, 2001). In this paper, we address the case in which the stations are arbitrarily located along a line (i.e., the linear case). We provide the first polynomial-time algorithm that returns an optimal solution for any instance of the linear case. The algorithm works in O(hN(2)) time. (C) 2002 Published by Elsevier Science B.V

Experimental Comparison of Algorithms for Energy-Efficient Multicasting in Ad Hoc Networks

“…Geometric cases of MEBT have received significant attention in the literature. When the nodes are points on a line, MEBT can be optimally solved in polynomial time [3,7]. The case where the nodes are points in the Euclidean plane has been much studied.…”

Energy efficient communication in ad hoc networks from user's and designer's perspective

“…Optimal algorithms based on dynamic programming for the problem of bounded-hop strong connectivity and the problem of bounded-hop broadcast on a line are presented by Kirousis et al [20] and Clementi at al. [11], respectively. Differently from [20,11], we consider the bounded-hop broadcast problem for a general topology.…”

“…[11], respectively. Differently from [20,11], we consider the bounded-hop broadcast problem for a general topology. Beier et al [3] and Funke et al [17] give efficient algorithms for finding a minimum-energy route between two given nodes that uses a bounded number of hops.…”

“…The unrestricted version of this problem is NP-hard [5]. For a line topology, this problem can be solved optimally using the dynamic programming algorithm of Clementi et al [11].…”

Dual Decomposition for Computational Optimization of Minimum-Power Shared Broadcast Tree in Wireless Networks

“…For the special case of 1-dimensional Euclidean space, RAP admits polynomial time algorithms [32,33]. Integer programming and approximation schemes have been investigated in [2].…”