TY - CHAP

T1 - Approximation algorithm for directed telephone multicast problem

AU - Elkin, Michael

AU - Kortsarz, Guy

PY - 2003/1/1

Y1 - 2003/1/1

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. The telephone k-multicast problem requires to compute a schedule with minimal number of rounds that delivers a message from a given single processor, that generates the message, to all the processors of a given set T ⊆ V, |T| = k. 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(max{log k, log n/log k} · br* + k1/2) rounds for the directed k-multicast problem, where br* is the value of the optimum solution. This significantly improves the previously best-known approximation ratio of O(k1/3 · log n · br* + k2/3) due to [EK03]. We show that our algorithm for the directed multicast problem can be used to derive an algorithm with a similar ratio for the directed minimum poise Steiner arborescence problem, that is, the problem of constructing an arborescence that spans a collection T of terminals, minimizing the sum of height of the arborescence plus maximum out-degree in the arborescence.

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. The telephone k-multicast problem requires to compute a schedule with minimal number of rounds that delivers a message from a given single processor, that generates the message, to all the processors of a given set T ⊆ V, |T| = k. 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(max{log k, log n/log k} · br* + k1/2) rounds for the directed k-multicast problem, where br* is the value of the optimum solution. This significantly improves the previously best-known approximation ratio of O(k1/3 · log n · br* + k2/3) due to [EK03]. We show that our algorithm for the directed multicast problem can be used to derive an algorithm with a similar ratio for the directed minimum poise Steiner arborescence problem, that is, the problem of constructing an arborescence that spans a collection T of terminals, minimizing the sum of height of the arborescence plus maximum out-degree in the arborescence.

UR - http://www.scopus.com/inward/record.url?scp=33749657468&partnerID=8YFLogxK

U2 - 10.1007/3-540-45061-0_19

DO - 10.1007/3-540-45061-0_19

M3 - Chapter

AN - SCOPUS:33749657468

SN - 3540404937

SN - 9783540404934

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 212

EP - 223

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Baeten, Jos C. M.

A2 - Lenstra, Jan Karel

A2 - Parrow, Joachim

A2 - Woeginger, Gerhard J.

PB - Springer Verlag

ER -