How to Allocate Network Centers

Bar‐Ilan, Judit; Kortsarz, Guy; Peleg, David

doi:10.1006/jagm.1993.1047

Cited by 154 publications

(140 citation statements)

References 9 publications

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“…When the capacities are uniform, Khuller and Sussmann [17], using the technique of Bar-Ilan, Kortsarz, and Peleg [4], gives a 13-approximation algorithm. In this subsection, we present a 9-approximation algorithm for the budgeted center problem with uniform capacities.…”

Section: Budgeted Version With Uniform Capacitiesmentioning

confidence: 99%

Centrality of Trees for Capacitated k-Center

Bhaskara

Chekuri

et al. 2014

Integer Programming and Combinatorial Optimization

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We consider the capacitated k-center problem. In this problem we are given a finite set of locations in a metric space and each location has an associated non-negative integer capacity. The goal is to choose (open) k locations (called centers) and assign each location to an open center to minimize the maximum, over all locations, of the distance of the location to its assigned center. The number of locations assigned to a center cannot exceed the center's capacity. The uncapacitated k-center problem has a simple tight 2-approximation from the 80's. In contrast, the first constant factor approximation for the capacitated problem was obtained only recently by Cygan, Hajiaghayi and Khuller who gave an intricate LP-rounding algorithm that achieves an approximation guarantee in the hundreds. In this paper we give a simple algorithm with a clean analysis and prove an approximation guarantee of 9. It uses the standard LP relaxation and comes close to settling the integrality gap (after necessary preprocessing), which is narrowed down to either 7, 8 or 9. The algorithm proceeds by first reducing to special tree instances, and then uses our best-possible algorithm to solve such instances. Our concept of tree instances is versatile and applies to natural variants of the capacitated k-center problem for which we also obtain improved algorithms. Finally, we give evidence to show that more powerful preprocessing could lead to better algorithms, by giving an approximation algorithm that beats the integrality gap for instances where all non-zero capacities are the same.

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Section: Budgeted Version With Uniform Capacitiesmentioning

confidence: 99%

Centrality of Trees for Capacitated k-Center

Bhaskara

Chekuri

et al. 2014

Integer Programming and Combinatorial Optimization

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“…This algorithm requires O(kn) distance computations. 4] gave the rst polynomial time approximation algorithm for the capacitated k-center problem, achieving an approximation factor of 10. They also proposed an approximation algorithm for the capacitated problem with xed cluster size.…”

Section: Introductionmentioning

confidence: 99%

Exact and Approximation Algorithms for Clustering

2002

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In this paper we present a n O(k 1 1=d ) time algorithm for solving the k-center problem in R d , under L 1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete k-center problem, as well. We also describe a simple (1 + )-approximation algorithm for the k-center problem, with running time O(n log k) + (k= ) O(k 1 1=d ) . Finally, we present a n O(k 1 1=d ) time algorithm for solving the L-capacitated k-center problem, provided that L = (n=k 1 1=d ) or L = O(1). We conclude with a simple approximation algorithm for the L-capacitated k-center problem.

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“…Clustering has been used by several algorithms for the k-center problem, for both the capacitated [2,16] and fault-tolerant cases [3,4,15,17]. We use the construction considered by Khuller and Sussmann [16].…”

Section: Dealing With the Integrality Gapmentioning

confidence: 99%

“…LetR ⊆V be the set corresponding to vector y (2) . First consider a bipartite graph (2) (X (2) (U )) ≥ |U |. This is exactly Hall's condition for the existence of a matching in H covering V .…”

Section: Lemma 8 Consider F ⊆ B With |F | = α and Let R Be The Integmentioning

confidence: 99%

Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

Fernandes

Paula

Pedrosa

2016

LATIN 2016: Theoretical Informatics

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In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center. One of the most general variants is the capacitated α-faulttolerant k-center, where centers have a limit on the number of assigned elements, and, if α centers fail, there is a reassignment from V to non-faulty centers. In this paper, we present a new approach to tackle fault tolerance, by selecting and pre-opening a set of backup centers, then solving the obtained residual instance. For the {0, L}-capacitated case, we give approximations with factor 6 for the basic problem, and 7 for the so called conservative variant, when only clients whose centers failed may be reassigned. Our algorithms improve on the previously best known factors of 9 and 17, respectively. Moreover, we consider the case with general capacities. Assuming α is constant, our method leads to the first approximations for this case. We also derive approximations for the capacitated fault-tolerant k-supplier problem.

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How to Allocate Network Centers

Cited by 154 publications

References 9 publications

Centrality of Trees for Capacitated k-Center

Centrality of Trees for Capacitated k-Center

Exact and Approximation Algorithms for Clustering

Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

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