TY - JOUR

T1 - Time bounds on fault‐tolerant broadcasting

AU - Peleg, David

AU - Schäffer, Alejandro A.

PY - 1989/12

Y1 - 1989/12

N2 - Broadcasting is the process by which a message originated at one vertex is delivered to all other vertices of a network, subject to the restriction that a vertex may participate in only one message transfer during a given time unit. A k fault‐tolerant broadcasting scheme is a calling scheme that gurantees the completion of the broadcast in the presence of up to k link failures. Let Tk(n) denote the minimum time required for k fault‐tolerant broadcasting in an n‐vertex network. Liestman [Networks 15 (1985) 159–171] showed that for every n and k such that n − 2 ≥ k ≥ 1, Tk(n) ⩾ [log n]+k. This paper establishes a matching upper bound, showing that for such n and k, Tk(n) ϵ O (log n +k). In particular, we present various efficient broadcasting schemes achieving almost optimal multiplicative constants. Our best upper bound uses new partial results on a tree‐packing problem that may be of independent interest.

AB - Broadcasting is the process by which a message originated at one vertex is delivered to all other vertices of a network, subject to the restriction that a vertex may participate in only one message transfer during a given time unit. A k fault‐tolerant broadcasting scheme is a calling scheme that gurantees the completion of the broadcast in the presence of up to k link failures. Let Tk(n) denote the minimum time required for k fault‐tolerant broadcasting in an n‐vertex network. Liestman [Networks 15 (1985) 159–171] showed that for every n and k such that n − 2 ≥ k ≥ 1, Tk(n) ⩾ [log n]+k. This paper establishes a matching upper bound, showing that for such n and k, Tk(n) ϵ O (log n +k). In particular, we present various efficient broadcasting schemes achieving almost optimal multiplicative constants. Our best upper bound uses new partial results on a tree‐packing problem that may be of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=84986938680&partnerID=8YFLogxK

U2 - 10.1002/net.3230190706

DO - 10.1002/net.3230190706

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AN - SCOPUS:84986938680

SN - 0028-3045

VL - 19

SP - 803

EP - 822

JO - Networks

JF - Networks

IS - 7

ER -