TY - JOUR

T1 - An approximation algorithm for the directed telephone multicast problem

AU - Elkin, Michael

AU - Kortsarz, Guy

PY - 2006/8

Y1 - 2006/8

N2 - Consider a network of processors modeled by an n-vertex directed graph G = (V,E). Assume that the communication in the network is synchronous, i.e., occurs in discrete "rounds," and in every round every processor is allowed to pick one of its neighbors, and to send him a message. A set of terminals T V of size |T| = k is given. The telephone k-multicast} problem requires computing a schedule with a minimal number of rounds that delivers a message from a given single processor, that generates the message, to all the processors of T. The processors of V\T may be left uninformed. The telephone multicast is a basic primitive in distributed computing and computer communication theory. In this paper we devise an algorithm that constructs a schedule with O(log k • b* + k1/2) rounds for the directed k-multicast} problem, where b* is the value of the optimum solution. This is the first algorithm with a non-trivial approximation guarantee for this problem. We show that our algorithm for the directed multicast problem can be used to derive an algorithm with a similar ratio for the directed Steiner poise problem, that is, the problem of constructing an arborescence that spans a collection T of terminals and has the minimum poise.

AB - Consider a network of processors modeled by an n-vertex directed graph G = (V,E). Assume that the communication in the network is synchronous, i.e., occurs in discrete "rounds," and in every round every processor is allowed to pick one of its neighbors, and to send him a message. A set of terminals T V of size |T| = k is given. The telephone k-multicast} problem requires computing a schedule with a minimal number of rounds that delivers a message from a given single processor, that generates the message, to all the processors of T. The processors of V\T may be left uninformed. The telephone multicast is a basic primitive in distributed computing and computer communication theory. In this paper we devise an algorithm that constructs a schedule with O(log k • b* + k1/2) rounds for the directed k-multicast} problem, where b* is the value of the optimum solution. This is the first algorithm with a non-trivial approximation guarantee for this problem. We show that our algorithm for the directed multicast problem can be used to derive an algorithm with a similar ratio for the directed Steiner poise problem, that is, the problem of constructing an arborescence that spans a collection T of terminals and has the minimum poise.

KW - Approximation

KW - Broadcast

KW - Directed

UR - http://www.scopus.com/inward/record.url?scp=33746218120&partnerID=8YFLogxK

U2 - 10.1007/s00453-005-1196-4

DO - 10.1007/s00453-005-1196-4

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AN - SCOPUS:33746218120

SN - 0178-4617

VL - 45

SP - 569

EP - 583

JO - Algorithmica

JF - Algorithmica

IS - 4

ER -