TY - JOUR

T1 - Polylogarithmic additive inapproximability of the radio broadcast problem

AU - Elkin, Michael

AU - Kortsarz, Guy

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2005

Y1 - 2005

N2 - The input for the radio broadcast problem is an undirected n-vertex graph G and a source node s. The goal is to send a message from s to the rest of the vertices in the minimum number of rounds. In a round, a vertex receives the message only if exactly one of its neighbors transmits. The radio broadcast problem admits an O(log 2 n) approximation [I. Chlamtac and O. Weinstein, in Proceedings of the IEEE INFOCOM, 1987, pp. 874-881; D. Kowalski and A. Pelc, in APPROX-RANDOM, Lecture Notes in Comput. Sci. 3122, Springer, Berlin, 2004, pp. 171-182]. In this paper we consider the additive approximation ratio of the problem. We prove that there exists a constant c so that the problem cannot be approximated within an additive term of c log 2 n, unless N P ⊆ BTIME(n O(log log n)).

AB - The input for the radio broadcast problem is an undirected n-vertex graph G and a source node s. The goal is to send a message from s to the rest of the vertices in the minimum number of rounds. In a round, a vertex receives the message only if exactly one of its neighbors transmits. The radio broadcast problem admits an O(log 2 n) approximation [I. Chlamtac and O. Weinstein, in Proceedings of the IEEE INFOCOM, 1987, pp. 874-881; D. Kowalski and A. Pelc, in APPROX-RANDOM, Lecture Notes in Comput. Sci. 3122, Springer, Berlin, 2004, pp. 171-182]. In this paper we consider the additive approximation ratio of the problem. We prove that there exists a constant c so that the problem cannot be approximated within an additive term of c log 2 n, unless N P ⊆ BTIME(n O(log log n)).

KW - Approximation

KW - Broadcast

KW - Radio

UR - http://www.scopus.com/inward/record.url?scp=33751179464&partnerID=8YFLogxK

U2 - 10.1137/S0895480104445319

DO - 10.1137/S0895480104445319

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33751179464

SN - 0895-4801

VL - 19

SP - 881

EP - 899

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 4

ER -