Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph
TL;DR: In this article, the generalized vertex median of a weighted graph may be found by complete enumeration or by some heuristic method, and a method that seems to perform well in comparison with others found in the literature is proposed.
Abstract: The generalized vertex median of a weighted graph may be found by complete enumeration or by some heuristic method. This paper investigates alternatives and proposes a method that seems to perform well in comparison with others found in the literature.
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TL;DR: This chapter presents the basic schemes of VNS and some of its extensions, and presents five families of applications in which VNS has proven to be very successful.
3,572 citations
TL;DR: This review reports on literature which explicitly addresses the strategic nature of facility location problems by considering either stochastic or dynamic problem characteristics, with applications ranging across numerous industries.
1,321 citations
22 Apr 2001
TL;DR: This work develops several placement algorithms that use workload information, such as client latency and request rates, to make informed placement decisions, and evaluates the placement algorithms using both synthetic and real network topologies, as well as Web server traces.
Abstract: There has been an increasing deployment of content distribution networks (CDNs) that offer hosting services to Web content providers. CDNs deploy a set of servers distributed throughout the Internet and replicate provider content across these servers for better performance and availability than centralized provider servers. Existing work on CDNs has primarily focused on techniques for efficiently redirecting user requests to appropriate CDN servers to reduce request latency and balance load. However, little attention has been given to the development of placement strategies for Web server replicas to further improve CDN performance. We explore the problem of Web server replica placement in detail. We develop several placement algorithms that use workload information, such as client latency and request rates, to make informed placement decisions. We then evaluate the placement algorithms using both synthetic and real network topologies, as well as Web server traces, and show that the placement of Web replicas is crucial to CDN performance. We also address a number of practical issues when using these algorithms, such as their sensitivity to imperfect knowledge about client workload and network topology, the stability of the input data, and methods for obtaining the input.
895 citations
TL;DR: This paper forms reliability models based on both the PMP and the UFLP and presents an optimal Lagrangian relaxation algorithm to solve them, and discusses how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account.
Abstract: Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that, once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost, while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account, and we use these trade-off curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.
703 citations
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TL;DR: It is shown that the optimum location of a switching center is always at a vertex of the communication network while the best location for the police station is not necessarily at an intersection.
Abstract: The concepts of the "center" and the "median vertex" of a graph are generalized to the "absolute center" and the "absolute median" of a weighted graph a graph with weights attached to its vertices as well as to its branches. These results are used to find the optimum location of a "switching center" in a communication network and to locate the best place to build a "police station" in a highway system. It is shown that the optimum location of a switching center is always at a vertex of the communication network while the best location for the police station is not necessarily at an intersection. Procedures for finding these locations are given.
2,224 citations
TL;DR: It is shown that the optimum distribution of p switching centers in a communication network is at a p-median of the corresponding weighted graph.
Abstract: The concept of a median in a weighted graph is generalized to a multimedian. Then, it is shown that the optimum distribution of p switching centers in a communication network is at a p-median of the corresponding weighted graph. The following related problem in highway networks is also considered: What is a minimum number of policemen that can be distributed in a highway network so that no one is farther away from a policeman than a given distance d? This problem is attacked by generating all vertex-coverings externally stable sets of a graph by means of a Boolean function defined over the vertices of a graph. Then this idea is extended to Boolean functions that generate all matchings, all factors, and all possible subgraphs of G with given degrees.
1,076 citations
TL;DR: The calculational aspects of solving certain classes of location-allocation problems are presented in this article, where exact extremal equations and a heuristic method are presented for solving these problems, and directions for further investigation are also indicated because of the need for methods to shorten the total amount of calculation involved.
Abstract: The calculational aspects of solving certain classes of location-allocation problems are presented. Both exact extremal equations and a heuristic method are presented for solving these problems. Directions for further investigation are also indicated because of the need for methods to shorten the total amount of calculation involved.
856 citations
500 citations
IBM1
TL;DR: An algorithm applicable to the problem of locating supply points optimally with respect to transport costs is given and may fail to converge to an optimal solution.
Abstract: An algorithm applicable to the problem of locating supply points optimally with respect to transport costs is given.Although the algorithm may fail to converge to an optimal solution, repeated appl...
363 citations