The forwarding index of communication networks

Chung, Fan; Coffman, E. G.; Reiman, Martin I.; Simon, Burton

doi:10.1109/tit.1987.1057290

Cited by 95 publications

(68 citation statements)

References 2 publications

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“…This result gives a partial solution of the problem raised by Chung et al [16]: designing and analyzing networks with given maximum degree which have minimum or near-minimum forwarding indices (see Section 4 in this paper for details).…”

Section: Optimal Graphsmentioning

confidence: 91%

“…The following bounds of ξ(G) and π(G) were first established by Chung et al [16] and Heydemann et al [32], respectively. Theorem 2.3 (Chung et al [16], 1987).…”

Section: Basic Bounds and Relationsmentioning

confidence: 95%

“…In 1987, Chung et al [16] asked whether the problem of computing the forwarding index of a graph is an NP-complete problem. Following [22], we state this problem as the following decision problem.…”

Section: Np-completenessmentioning

confidence: 99%

“…The original research of the forwarding indices is motivated by the problem of maximizing network capacity [16]. Maximizing network capacity clearly reduces to minimizing vertex-forwarding index or edge-forwarding index of a routing.…”

Section: Introductionmentioning

confidence: 99%

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The forwarding indices of graphs - a survey

2013

OpMath

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Abstract. A routing R of a connected graph G of order n is a collection of n(n − 1) simple paths connecting every ordered pair of vertices of G. The vertex-forwarding index ξ(G, R) of G with respect to a routing R is defined as the maximum number of paths in R passing through any vertex of G. The vertex-forwarding index ξ(G) of G is defined as the minimum ξ(G, R) over all routings R of G. Similarly, the edge-forwarding index π(G, R) of G with respect to a routing R is the maximum number of paths in R passing through any edge of G. The edge-forwarding index π(G) of G is the minimum π(G, R) over all routings R of G. The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory.

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Section: Optimal Graphsmentioning

confidence: 91%

“…The following bounds of ξ(G) and π(G) were first established by Chung et al [16] and Heydemann et al [32], respectively. Theorem 2.3 (Chung et al [16], 1987).…”

Section: Basic Bounds and Relationsmentioning

confidence: 95%

Section: Np-completenessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The forwarding indices of graphs - a survey

2013

OpMath

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“…Given the amount of traffic flowing between processors, the problem of choosing the right combination of routing function and processor topology seems to be a difficult problem due to the complex interplay between topology and routing function. This problem might be formulated in terms of finding a minimum forwarding index routing [30]. For a given set of source-destination pairs, a minimum forwarding index routing is a routing that minimizes the maximum number of paths that pass through any given vertex.…”

Section: Other Optimization Techniques and Criteriamentioning

confidence: 99%

Synthesizing minimum total expansion topologies for reconfigurable interconnection networks

Smitley

Lee

1989

Journal of Parallel and Distributed Computing

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The Performance of a parallel algorithm depends in part on how the interconnection topology of the target parallel system matches the communication patterns of the algorithm. We describe how to generate a topology for a network that can be configured into and r-regular topology. The topology generated has small total expansion with respect to a given task graph. The expansion of an edge in a task graph is the length of the shortest path that the edge maps to in the processor graph. The algorithm used to generate the topologies is analyzed and its average case behavior is determined. In addition, this synthesis method is compared to the conventional approach of mapping a task graph onto a fixed processor topology. ABSTRACT The performance of a parallel algorithm depends in part on how well the interconnection topology of the target parallel system matches the communication patterns of the algorithm. We describe how to generate a topology for a network that can be configured into any r-regular topology. The topology generated has small total expansion with respect to a given task graph. The expansion of an edge in a task graph is the length of the shortest path that the edge maps to in the processor graph. The algorithm used to generate the topologies is analyzed and its average case behavior is determined. In addition, this synthesis method is compared to the conventional approach of mapping a task graph onto a fixed processor topology.-3 -Symbols

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Low-congested interval routing schemes for hypercubelike networks

2000

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In this paper, we provide low‐congested interval routing schemes (IRS) for some common interconnection networks such as butterflies, wrapped butterflies, and cube‐connected cycles. In particular, by exploiting their hypercubelike structure, we show that 1‐IRS and 2‐IRS are already sufficient to get schemes with a congestion which is at most c times the optimal one, for low constant values of c. All such schemes have also a small dilation proportional to the diameter. Moreover, a new lower bound on the congestion achievable by schemes for butterfly networks is provided, which improves upon the best previously known one [25]. © 2000 John Wiley & Sons, Inc.

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The forwarding index of communication networks

Cited by 95 publications

References 2 publications

The forwarding indices of graphs - a survey

The forwarding indices of graphs - a survey

Synthesizing minimum total expansion topologies for reconfigurable interconnection networks

Low-congested interval routing schemes for hypercubelike networks

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