Optimal Center Location in Simple Networks

Goldman, A. J.

doi:10.1287/trsc.5.2.212

Cited by 351 publications

(150 citation statements)

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“…This problem is called the 1-median problem on a tree. Goldman [25] showed that the problem can be solved in O(n) time, where n is the number of nodes in the tree: Begin with any tip node of the tree. If the demand at that node is equal to or greater than half the total demand of all nodes, the optimal location is at that node.…”

Section: A Taxonomy Of Location Modelsmentioning

confidence: 99%

What you should know about location modeling

Daskin

2008

Naval Research Logistics

203

110

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Facility location models have been applied to problems in the public and private sectors for years. In this article, the author first presents a taxonomy of location problems based on the underlying space in which the problem is embedded. The article illustrates problems from each part of the taxonomy with an emphasis on discrete location problems. Selected recent research in the area is also discussed.

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Section: A Taxonomy Of Location Modelsmentioning

confidence: 99%

What you should know about location modeling

Daskin

2008

Naval Research Logistics

203

110

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“…, n (cf. Goldman [8]). In case of the unweighted 1-center problem, it is easy to see that the above optimality criterion is equivalent to the so-called midpoint property, i.e., the 1-center lies on the midpoint of a longest path.…”

Section: Convex Ordered Median Problems On Treesmentioning

confidence: 99%

An inverse approach to convex ordered median problems in trees

Gassner

2010

J Comb Optim

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The convex ordered median problem is a generalization of the median, the k-centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP-hard even if the underlying network is a tree and the ordered median problem is convex and either the vertex weights are all equal to 1 or the underlying problem is the k-centrum problem. For the special case of the inverse unit weight k-centrum problem a polynomial time algorithm is developed.

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“…[GOLD71] gave an O(n), a linear time, algorithm for solving 1-median problem on a tree. [KARI79] provided an O(n 2 k 2 ) algorithm for finding k medians on a tree with n nodes.…”

Section: 313mentioning

confidence: 99%

A Clustering-Based Selective Probing Framework to Support Internet Quality of Service Routing

Jariyakul

Znati

2005

Distributed Computing – IWDC 2005

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The advent of the multimedia applications has triggered widespread interest in QoS supports. Two Internet-based QoS frameworks have been proposed: Integrated Services (IntServ) and Differentiated Services (DiffServ). IntServ supports service guarantees on a per-flow basis. The framework, however, is not scalable due to the fact that routers have to maintain a large amount of state information for each supported flow. DiffServ was proposed as an alternate solution to address the lack of scalability of the IntServ framework. DiffServ uses class-based service differentiation to achieve aggregate support for QoS requirements. This approach eliminates the need to maintain per-flow states on a hop-by-hop basis and reduces considerably the overhead routers incur in forwarding traffic.Both IntServ and DiffServ frameworks focus on packet scheduling. As such, they decouple routing from QoS provisioning. This typically results in inefficient routes, thereby limiting the ability of the network to support QoS requirements and to manage resources efficiently. The goal of this thesis is to address this shortcoming. We propose a scalable QoS routing framework to identify and select paths that are very likely to meet the QoS requirements of the underlying applications. The tenet of our approach is based on seamlessly integrating routing into the DiffServ framework to extend its ability to support QoS requirements. Scalability is achieved using selective probing and clustering to reduce signaling and routers overhead.The major contributions of this thesis are as follows: First, we propose a scalable routing architecture that supports QoS requirements. The architecture seamlessly integrates the QoS traffic requirements of the underlying applications into a DiffServ framework. Second, we propose a new delay-based clustering method, referred to as d-median. The proposed clustering method groups Internet nodes into clusters, whereby nodes in the same cluster exhibit equivalent delay characteristics. Each cluster is represented by anchor node. Anchors use selective probing to estimate QoS parameters and select appropriate paths for traffic forwarding.A thorough study to evaluate the performance of the proposed d-median clustering algorithm is conducted. The results of the study show that, for power-law graphs such as the Internet, the d-median clustering based approach outperforms the set covering method commonly proposed in the literature. The study shows that the widely used clustering methods, such as set covering or k-median, are inadequate to capture the balance between cluster sizes and the number of clusters. The results of the study also show that the proposed clustering method, applied to power-law graphs, is robust to changes in size and delay distribution of the network. Finally, the results suggest that the delay bound input parameter of the d-median scheme should be no less than 1 and no more than 4 times of the average delay per one hop of the network. This is mostly due to the weak hierarchy of the Internet resulting fr...

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Optimal Center Location in Simple Networks

Cited by 351 publications

References 1 publication

What you should know about location modeling

What you should know about location modeling

An inverse approach to convex ordered median problems in trees

A Clustering-Based Selective Probing Framework to Support Internet Quality of Service Routing

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