Journal•ISSN: 0028-3045

# Networks

Wiley-Blackwell

About: Networks is an academic journal published by Wiley-Blackwell. The journal publishes majorly in the area(s): Shortest path problem & Flow network. It has an ISSN identifier of 0028-3045. Over the lifetime, 2469 publications have been published receiving 89850 citations.

Topics: Shortest path problem, Flow network, Time complexity, Vehicle routing problem, Steiner tree problem

##### Papers published on a yearly basis

##### Papers

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TL;DR: Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network as discussed by the authors, and the results that have been obtained on these and related problems.

Abstract: Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping every person in the network knows a unique item of information and needs to communicate it to everyone else. In broadcasting one individual has an item of information which needs to be communicated to everyone else. We review the results that have been obtained on these and related problems.

1,191 citations

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TL;DR: This paper presents a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost and shows that it has outperformed the best existing heuristics on a sample of standard test problems.

Abstract: : We consider a common variant of the vehicle routing problem in which a vehicle fleet delivers products stored at a central depot to satisfy customer orders. Each vehicle has a fixed capacity, and each order uses a fixed portion of vehicle capacity. The routing decision involves determining which of the demands will be satisfied by each vehicle and what route each vehicle will follow in servicing its assigned demand in order to minimize total delivery cost. We present a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost. This heuristic has many attractive features. It has outperformed the best existing heuristics on a sample of standard test problems. It will always find a feasible solution if one exists, something no other existing heuristic can guarantee. It can be easily adapted to accommodate many additional problem complexities. By parametrically varying the number of vehicles in the fleet, our method can be used to optimally solve the problem of finding the minimum size fleet that can feasibly service the specified demand.

1,050 citations

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TL;DR: In this paper, the complexity of a class of vehicle routing and scheduling problems is investigated, and the results on the worst-case performance of approximation algorithms are discussed and some directions for future research are suggested.

Abstract: The complexity of a class of vehicle routing and scheduling problems is investigated. We review known NP-hardness results and compile the results on the worst-case performance of approximation algorithms. Some directions for future research are suggested. The presentation is based on two discussion sessions during the Workshop to Investigate Future Directions in Routing and Scheduling of Vehicles and Crews, held at the University of Maryland at College Park, June 4–6, 1979.

1,017 citations

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TL;DR: In this article, a tabu search heuristic was proposed for solving three well-known routing problems: the periodic vehicle routing problem, the periodic traveling salesman problem, and the multi-depot vehicle routing problems.

Abstract: We propose a tabu search heuristic capable of solving three well-known routing problems: the periodic vehicle routing problem, the periodic traveling salesman problem, and the multi-depot vehicle routing problem. Computational experiments carried out on instances taken from the literature indicate that the proposed method outperforms existing heuristics for all three problems. © 1997 John Wiley & Sons, Inc. Networks 30: 105–119, 1997

826 citations

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Bell Labs

^{1}TL;DR: This paper considers the problem of finding, for each possible sink vertex v, a pair of edge-disjoint paths from s to v of minimum total edge cost, and gives an implementation of Suurballe's algorithm that runs in O(m log(1+ m/n)n) time and O( m) space.

Abstract: Let G be a directed graph containing n vertices, one of which is a distinguished source s, and m edges, each with a non-negative cost. We consider the problem of finding, for each possible sink vertex v, a pair of edge-disjoint paths from s to v of minimum total edge cost. Suurballe has given an O(n2 logn)-time algorithm for this problem. We give an implementation of Suurballe's algorithm that runs in O(m log(1+ m/n)n) time and O(m) space. Our algorithm builds an implicit representation of the n pairs of paths; given this representation, the time necessary to explicitly construct the pair of paths for any given sink is O(1) per edge on the paths.

758 citations