Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes

Hromkovič, Juraj; Klasing, Ralf; Unger, Walter; Wagener, Hubert

doi:10.1006/inco.1996.2618

Cited by 18 publications

(6 citation statements)

References 13 publications

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“…Several known bounds are summarised as follows (see [6] for the EDP mode and [8] for the VDP mode): Lemma 1. Let G be a network of n nodes, of edge-bisection ew(G) and of vertex-bisection vw(G).…”

Section: Theoremmentioning

confidence: 99%

Random Walks and Bisections in Random Circulant Graphs

Mans

Shparlinski

2012

LATIN 2012: Theoretical Informatics

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Abstract. Using number theoretical tools, we prove two main results for random r-regular circulant graphs with n vertices, when n is sufficiently large and r is fixed. First, for any fixed ε > 0, prime n and L ≥ n 1/r (log n) 1+1/r+ε , walks of length at most L terminate at every vertex with asymptotically the same probability. Second, for any n, there is a polynomial time algorithm to find a vertex bisector and an edge bisector, both of size less than n 1−1/r+o(1) . As circulant graphs are popular network topologies in distributed computing, we show that our results can be exploited for various information dissemination schemes. In particular, we provide lower bounds on the number of rounds required by any gossiping algorithms for any n.This settles an open question in an earlier work of the authors (2004) and shows that the generic gossiping algorithms of that work are nearly optimal.

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Section: Theoremmentioning

confidence: 99%

Random Walks and Bisections in Random Circulant Graphs

Mans

Shparlinski

2012

LATIN 2012: Theoretical Informatics

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“…However, although this algorithm can be extended to the multicast problem in which the set of destinations is a subset of the nodes of the tree, it yields an ine cient protocol. In the 1-port line model, Farley Far80] has shown that every undirected n-node network has a broadcast time of dlog 2 ne (see also HKUW97]). This result has been extended in CFKR98] to the case in which the routes are chosen according to a shortest path routing function.…”

Section: Previous Workmentioning

confidence: 99%

Minimal contention-free matrices with application to multicasting

Cohen¹,

Fraigniaud²,

Riera³

2000

Robust Communication Networks: Interconnection and Survivability

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Abstract. In this paper, we s h o w that the multicast problem in trees can be expressed in term of arranging rows and columns of boolean matrices. Given a p q matrix M with 0-1 entries, the shadow of M is de ned as a boolean vector x of q entries such t h a t x i = 0 if and only if there is no 1-entry in the ith column of M, and x i = 1 otherwise. (The shadow x can also be seen as the binary expression of the integer x = P q i=1 x i 2 q;i . Similarly, e v ery row of M can be seen as the binary expression of an integer.) According to this formalism, the key for solving a multicast problem in trees is shown to be the following. Given a p q matrix M with 0-1 entries, nding a matrix M such that:1. M has at most one 1-entry per column 2. every row r of M (viewed as the binary expression of an integer) is larger than the corresponding row r of M, 1 r p and 3. the shadow o f M (viewed as an integer) is minimum. We show that there is an O(q(p + q)) algorithm that returns M for any p q boolean matrix M.The application of this result is the following: Given a directed tree T whose arcs are oriented from the root toward the leaves, and a subset of nodes D, there exists a polynomial-time algorithm that computes an optimal multicast protocol from the root to all nodes of D in the all-port line model.

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“…Variants of both path and line broadcast models have been studied recently, primarily from the perspective of demonstrating that known, regular network topologies are minimal line or minimal path broadcast networks, often in the context of efficient wormhole routing [12,13].…”

Section: Introductionmentioning

confidence: 99%

Minimal path broadcast networks

Farley

2004

Networks

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Broadcasting is the communication process whereby a message that is initially known by one site becomes known to all sites of a network. Messages are transmitted by calls from senders to sets of receivers. In path broadcasting, a site can call nonneighboring sites over paths in the network. A call occupies all sites and edges on the path followed by the call; thus, any calls made concurrently must be vertex-disjoint. We discuss the design of sparse networks that allow path broadcasting to be completed in minimum time under three different path broadcast models.

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Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes

Cited by 18 publications

References 13 publications

Random Walks and Bisections in Random Circulant Graphs

Random Walks and Bisections in Random Circulant Graphs

Minimal contention-free matrices with application to multicasting

Minimal path broadcast networks

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