A Unified Algorithm for Designing Multidrop Teleprocessing Networks

Kershenbaum, Aaron; Chou, Wushow

doi:10.1109/tcom.1974.1092123

Cited by 55 publications

(11 citation statements)

References 10 publications

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“…Removing a link or relay from N may only violate a drop constraint, not an add constraint. This observation suggests adaptations of two standard algorithms (Kershenbaum and Chou, 1974).…”

Section: Lemma For a Set Of Verticesmentioning

confidence: 83%

Principles of Cost Minimisation in Wireless Networks

Grout

2005

J Heuristics

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“…Removing a link or relay from N may only violate a drop constraint, not an add constraint. This observation suggests adaptations of two standard algorithms (Kershenbaum and Chou, 1974).…”

Section: Lemma For a Set Of Verticesmentioning

confidence: 83%

Principles of Cost Minimisation in Wireless Networks

Grout

2005

J Heuristics

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“…As an MST is already the optimal solution if it is a feasible solution (capacity constraints are met), many simple heuristics consider edge weights and either construct a solution similar to an MST (e.g. the unified algorithm from Kershenbaum and Chou [24], or the modified Kruskal algorithm from Boorstyn and Frank [5]), or modify an infeasible MST solution (e.g. the start procedure of Elias and Ferguson [12]).…”

Section: Designing Heuristic Optimization Methods For Ocst Problemsmentioning

confidence: 99%

On Optimal Solutions for the Optimal Communication Spanning Tree Problem

Rothlauf

2009

Operations Research

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This paper presents an experimental investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem seeks a spanning tree that connects all the nodes and satisfies their communication requirements at a minimum total cost. The paper compares the properties of random trees to the properties of the best solutions for the OCST problem that are found using an evolutionary algorithm. The results show on average, that the optimal solution and the minimum spanning tree (MST) share a higher number of links than the optimal solution and a random tree. Furthermore, optimal solutions for OCST problems with randomly chosen distance weights share a higher number of links with an MST than OCST problems with Euclidean distance weights. This intuitive similarity between optimal solutions and MSTs suggests that some heuristic optimization methods for OCST problems might be improved by starting with an MST. Using an MST as starting solution for a greedy search in the tested cases either improves median running time up to a factor of 10 while finding solutions of the same quality, or increases solution quality up to a factor of 100 while using the same number of search steps in comparison to starting the greedy search from a random tree. Starting a local search, a simulated annealing approach, and a genetic algorithm from an MST increases solution quality up to a factor of three in comparison to starting from a random solution.

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“…Some of the other heuristics that use savings procedure to construct the tree include Elias and Ferguson [1974], Gavish [1991], Gavish and Altinkemer [1986], Kershenbaum [1974], Whitney [1970]. Construction procedures [Boorstyn and Frank 1977;Chandy and Russell 1972;Karnaugh 1976;Kershenbaum and Chou 1974;Martin 1967;McGregor and Shen 1977;Schneider and Zastrow 1982;Sharma and El-Bardai 1970] start with an empty tree and add the best edge or node to grow the tree. Improvement procedures [Elias and Ferguson 1974;Frank et al 1971;Karnaugh 1976;Kershenbaum et al 1980;Malik and Yu 1993] start with an initial feasible solution, usually obtained by running the Esau and Williams [1966] algorithm, and make improvements by adding and deleting edges as long as improvements are possible.…”

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design

Jothi

Raghavachari

2005

ACM Trans. Algorithms

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Given an undirected graph G = (V, E) with nonnegative costs on its edges, a root node r ∈ V , a set of demands D ⊆ V with demand v ∈ D wishing to route w(v) units of flow (weight) to r , and a positive number k, the Capacitated Minimum Steiner Tree (CMStT) problem asks for a minimum Steiner tree, rooted at r , spanning the vertices in D ∪ {r }, in which the sum of the vertex weights in every subtree connected to r is at most k. When D = V , this problem is known as the Capacitated Minimum Spanning Tree (CMST) problem. Both CMsT and CMST problems are NP-hard. In this article, we present approximation algorithms for these problems and several of their variants in network design. Our main results are the following:-We present a (γρ ST + 2)-approximation algorithm for the CMStT problem, where γ is the inverse Steiner ratio, and ρ ST is the best achievable approximation ratio for the Steiner tree problem. Our ratio improves the current best ratio of 2ρ ST + 2 for this problem. -In particular, we obtain (γ +2)-approximation ratio for the CMST problem, which is an improvement over the current best ratio of 4 for this problem. For points in Euclidean and rectilinear planes, our result translates into ratios of 3.1548 and 3.5, respectively. -For instances in the plane, under the L p norm, with the vertices in D having uniform weights, we present a nontrivial ( 7 5 ρ ST + 3 2 )-approximation algorithm for the CMStT problem. This translates into a ratio of 2.9 for the CMST problem with uniform vertex weights in the L p metric plane. Our

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A Unified Algorithm for Designing Multidrop Teleprocessing Networks

Abstract: optimal networks, IBM Syst.

Cited by 55 publications

References 10 publications

Principles of Cost Minimisation in Wireless Networks

Principles of Cost Minimisation in Wireless Networks

On Optimal Solutions for the Optimal Communication Spanning Tree Problem

Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design

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