The 2-facility centdian network problem

Pérez-Brito, Dionisio; Moreno-Pérez, José A.; Rodríguez-Martín, Inmaculada

doi:10.1016/s0966-8349(98)00057-6

Cited by 12 publications

(5 citation statements)

References 6 publications

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“…We note that the specialization of the above theorem for the unweighted case, i.e., when u i = w i = 1, for all i = 1, ..., n, can be obtained from the results in Pérez-Brito et al [13,14].…”

Section: A Finite Dominating Setmentioning

confidence: 99%

A polynomial algorithm for thep-centdian problem on a tree

1998

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The most common problems studied in network location theory are the p-median and the p-center models. The p-median problem on a network is concerned with the location of p points (medians) on the network, such that the total (weighted) distance of all the nodes to their respective nearest points is minimized. The p center problem is concerned with the location of p-points (centers) on the network, such that the maximum (weighted) distance of all the nodes to their respective nearest points is minimized.To capture more real world problems, and obtain a good way to trade-off minisum (efficiency) and minimax (equity) approaches, Halpern [5,6,7], introduced the centdian model, where the objective is to minimize a convex combination of the objective functions of the center and the median problems. In this paper we study the p-centdian problem on tree networks, and present the first polynomial time algorithm for this problem.

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Section: A Finite Dominating Setmentioning

confidence: 99%

A polynomial algorithm for thep-centdian problem on a tree

1998

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“…Hooker et al (1991) considered a theoretical result that extended the finite dominating sets of the single facility problems to the corresponding P-facility problems, and applied it to the P-facility centdian problem. It is not reasonable; therefore a counterexample has been given by Perez-Brito et al (1998). In this paper finally an optimal solution consisting of vertices and local centers is presented as a set of final solution for solving the 2-centdian on the network.…”

Section: The 2-facility Centdian Network Problem (Perez-brito Et Al mentioning

confidence: 99%

Demand Point Aggregation Analaysis for Location Models

Sadigh

Fallah

2009

Facility Location

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“…This process can be done in linear time by the method in Section 3. Via this process, the end points of all candidate paths and the possible locations of all lower and upper centdians are vertices [8,21].…”

Section: An O(n Log N)-time Algorithm For the 2-radiian Problemmentioning

confidence: 99%

“…For p = 1, it can be solved in linear time [9,23]. For p = 2, it can be solved in O(n 2 ) time, where n is the number of vertices in the given tree network [21,23]. Readers can refer to [5,11,20,24] for related researches about centdian.…”

Section: Introductionmentioning

confidence: 99%

The 2-radius and 2-radiian problems on trees

Wang

Chao

2008

Theoretical Computer Science

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In this paper, we consider two facility location problems on tree networks. One is the 2-radius problem, whose goal is to partition the vertex set of the given network into two non-empty subsets such that the sum of the radii of these two induced subgraphs is minimum. The other is the 2-radiian problem, whose goal is to partition the network into two non-empty subsets such that the sum of the centdian values of these two induced subgraphs is minimum. We propose an O(n)-time algorithm for the 2-radius problem on trees and an O(n log n)-time algorithm for the 2-radiian problem on trees, where n is the number of vertices in the given tree.

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The 2-facility centdian network problem

Cited by 12 publications

References 6 publications

A polynomial algorithm for thep-centdian problem on a tree

A polynomial algorithm for thep-centdian problem on a tree

Demand Point Aggregation Analaysis for Location Models

The 2-radius and 2-radiian problems on trees

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