Efficient Algorithms for the 2-Center Problems

Takaoka, Tadao

doi:10.1007/978-3-642-12165-4_41

Cited by 4 publications

(3 citation statements)

References 17 publications

(18 reference statements)

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“…Hence, many approximation algorithms [3,18,19,23,43,47] and inapproximability results [24,26,27] had been proposed for both problems. These two problems have many applications in the network location, clustering, and social networks [1,8,13,14,15,20,23,30,31,38,40,45,46,48,49,51].…”

Section: Introductionmentioning

confidence: 99%

Approximability results for the $p$-centdian and the converse centdian problems

Chen¹

2022

Discrete Mathematics &Amp; Theoretical Computer Science

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Given an undirected graph $G=(V,E)$ with a nonnegative edge length function and an integer $p$, $0 < p < |V|$, the $p$-centdian problem is to find $p$ vertices (called the {\it centdian set}) of $V$ such that the {\it eccentricity} plus {\it median-distance} is minimized, in which the {\it eccentricity} is the maximum (length) distance of all vertices to their nearest {\it centdian set} and the {\it median-distance} is the total (length) distance of all vertices to their nearest {\it centdian set}. The {\it eccentricity} plus {\it median-distance} is called the {\it centdian-distance}. The purpose of the $p$-centdian problem is to find $p$ open facilities (servers) which satisfy the quality-of-service of the minimum total distance ({\it median-distance}) and the maximum distance ({\it eccentricity}) to their service customers, simultaneously. If we converse the two criteria, that is given the bound of the {\it centdian-distance} and the objective function is to minimize the cardinality of the {\it centdian set}, this problem is called the converse centdian problem. In this paper, we prove the $p$-centdian problem is NP-Complete. Then we design the first non-trivial brute force exact algorithms for the $p$-centdian problem and the converse centdian problem, respectively. Finally, we design two approximation algorithms for both problems.

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Section: Introductionmentioning

confidence: 99%

Approximability results for the $p$-centdian and the converse centdian problems

Chen¹

2022

Discrete Mathematics &Amp; Theoretical Computer Science

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“…This is better than the straightforward methods of solving the two problems in O(n 2.575 ) (Zwick, 2002) and O(n 2.688 ) (Duan & Pettie, 2009) time bounds, respectively. Note that the 2-center GC problem is investigated by (Takaoka, 2010).…”

Section: Introductionmentioning

confidence: 99%

First International Conference on Resource Efficiency in Interorganizational Networks – ResEff 2013 –

Geldermann¹,

Schümann²

2013

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“…the two problems in O(n 2.575 ) ( (Zwick, 2002)) and O(n 2.688 ) ( (Duan and Pettie, 2009)) time bounds, respectively. Note that the 2-center GC problem is investigated by (Takaoka, 2010).…”

Section: Introductionmentioning

confidence: 99%

Efficient Graph Algorithms for Network Analysis

Shinn,

Takaoka

2013

Preprint

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Efficient Algorithms for the 2-Center Problems

Cited by 4 publications

References 17 publications

Approximability results for the $p$-centdian and the converse centdian problems

Approximability results for the $p$-centdian and the converse centdian problems

First International Conference on Resource Efficiency in Interorganizational Networks – ResEff 2013 –

Efficient Graph Algorithms for Network Analysis

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