Local Search Heuristics for <i>k</i>-Median and Facility Location Problems

Arya, Vijay; Garg, Naveen; Khandekar, Rohit; Meyerson, Adam; Munagala, Kamesh; Pandit, Vinayaka

doi:10.1137/s0097539702416402

Cited by 485 publications

(592 citation statements)

References 6 publications

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“…Any such good point has all γ|G 1 | neighbors in C 1 ∪ B. Then any two such good points share at least 2γ|G 1 …”

Section: Algorithm 3 Generating Interesting Blobsmentioning

confidence: 99%

“…Yet unfortunately, for most natural clustering objectives, finding the optimal solution to the objective function is NP-hard. As a consequence, there has been substantial work on approximation algorithms [18,14,9,15,1] with both upper and lower bounds on the approximability of these objective functions on worst case instances.Recently, Bilu and Linial [13] suggested an exciting, alternative approach aimed at understanding the complexity of clustering instances which arise in practice. Motivated by the fact that distances between data points in clustering instances are often based on a heuristic measure, they argue that interesting instances should be resilient to small perturbations in these distances.…”

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Clustering under Perturbation Resilience

Balcan

Liang

2012

Automata, Languages, and Programming

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Abstract. Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial [13] proposed analyzing objective based clustering problems under the assumption that the optimum clustering to the objective is preserved under small multiplicative perturbations to distances between points. The hope is that by exploiting the structure in such instances, one can overcome worst case hardness results.In this paper, we provide several results within this framework. For center-based objectives, we present an algorithm that can optimally cluster instances resilient to perturbations of factor (1 + √ 2), solving an open problem of Awasthi et al. [3]. For k-median, a center-based objective of special interest, we additionally give algorithms for a more relaxed assumption in which we allow the optimal solution to change in a small ǫ fraction of the points after perturbation. We give the first bounds known for k-median under this more realistic and more general assumption. We also provide positive results for min-sum clustering which is typically a harder objective than center-based objectives from approximability standpoint. Our algorithms are based on new linkage criteria that may be of independent interest.Additionally, we give sublinear-time algorithms, showing algorithms that can return an implicit clustering from only access to a small random sample.Key words. clustering, perturbation resilience, k-median clustering, min-sum clustering AMS subject classifications. 68Q25, 68Q32, 68T05, 68W25, 68W401. Introduction. Problems of clustering data from pairwise distance information are ubiquitous in science. A common approach for solving such problems is to view the data points as nodes in a weighted graph (with the weights based on the given pairwise information), and then to design algorithms to optimize various objective functions such as k-median or min-sum. For example, in the k-median clustering problem the goal is to partition the data into k clusters C i , giving each a center c i , in order to minimize the sum of the distances of all data points to the centers of their cluster. In the min-sum clustering approach the goal is to find k clusters C i that minimize the sum of all intra-cluster pairwise distances. Yet unfortunately, for most natural clustering objectives, finding the optimal solution to the objective function is NP-hard. As a consequence, there has been substantial work on approximation algorithms [18,14,9,15,1] with both upper and lower bounds on the approximability of these objective functions on worst case instances.Recently, Bilu and Linial [13] suggested an exciting, alternative approach aimed at understanding the complexity of clustering instances which arise in practice. Motivated by the fact that distances between data points in clustering instances are often based on a heuristic measure, they argue that interesting instances should be resilient to small perturbations in these distances. In particular, if small pertur...

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“…Any such good point has all γ|G 1 | neighbors in C 1 ∪ B. Then any two such good points share at least 2γ|G 1 …”

Section: Algorithm 3 Generating Interesting Blobsmentioning

confidence: 99%

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confidence: 99%

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Clustering under Perturbation Resilience

Balcan

Liang

2012

Automata, Languages, and Programming

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“…Various methods have been proposed [1,3]. However, most methods are not efficient enough to deal with large spatial datasets.…”

Section: Static Facility Location Searchingmentioning

confidence: 99%

“…The decision will be made based on the local populations and the capability of the limited resources. Various methods for the single type of facility location problem have been proposed for the above applications [1,2,3].…”

Section: Introductionmentioning

confidence: 99%

STFLS: A Heuristic Method for Static and Transportation Facility Location Allocation in Large Spatial Datasets

Wang

Luo³

2009

Advances in Artificial Intelligence

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Abstract. This paper solves a static and transportation facility location allocation problem defined as follows: given a set of locations Loc and a set of demand objects D located in Loc, the goal is to allocate a set of static facilities S and a set of transportation facilities T to the locations in Loc, which minimizes both the average travelling distance from D to S and the maximum transportation travelling distance between D and S through T. The problem is challenging because two types of facilities are involved and cooperate with each other. In this paper, we propose a static and transportation facility location allocation algorithm, called STFLS, to solve the problem. The method uses two steps of searching for static facility and transportation facility locations Experiments demonstrate the efficiency and practicality of the algorithm.

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Content Replication and Delivery in Information‐Centric Networks

Sourlas

Flegkas

Katsaros

2014

Advanced Content Delivery, Streaming, and Cloud Services

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INTRODUCTIONInformation-centric networking (ICN) is emerging as the main future networking environment, given that the vast majority of Internet activities are related to information access and delivery. In ICN, information is explicitly labeled so that anybody who has relevant information can potentially participate in the fulfillment of requests for said information. Publications are issued by clients (publishers) when they have a new information item to publish in the network, while subscriptions are issued by clients (subscribers) to subscribe the items they are interested in. Given the information-centric nature of the distribution utilizing information that is replicated across almost ubiquitously, available storage devices are an almost natural thought. Optimized dissemination of information within transient communication relationships of endpoints is the main promise of such efforts, and efficient replication of information is key to delivering on this promise.While packet-level in-network opportunistic caching is one of the salient characteristics of ICN architectures, proper cache placement and replica assignment still have an important role to play. Content delivery network (CDN)-like replication distributes a Advanced Content Delivery, Streaming, and Cloud Services, First Edition. Edited by Mukaddim Pathan, Ramesh K. Sitaraman, and Dom Robinson. 414 CONTENT REPLICATION AND DELIVERY IN INFORMATION-CENTRIC NETWORKSsite's content across multiple mirror servers. When a client is interested in a particular piece of information, his/her request is redirected to one of the existing replication points rather than requiring retrieval from the original publisher. Replication is used to increase availability and fault tolerance, while it has as side-effect load-balancing and enhanced publisher subscriber proximity. Particularly, CDN providers strategically place surrogate servers and connect them to Internet service provider (ISP) network edges so that content can be closer to clients. Given the significant impact that content delivery has on the utilization of an ISP network, some work has recently started to investigate new models and frameworks to support the interaction between ISPs and CDNs.CDNs and ICN are designed to fulfill the necessity of efficient content delivery. Their main difference is that CDNs build up the end-to-end content delivery in the Internet at the application layer, while ICN is a clean slate proposal for an alternative approach to the core architecture of the network. In this chapter, we present a three-phase framework as a contribution to the problem of information replication in an ICN environment, through the synergy of ICN with CDN techniques. Moreover, we believe that this synergy will enable CDNs to incorporate, through the ICN functional components, dynamic network information on replica selection to determine the best paths over which transfer of content will take place. The objective of the presented framework is to minimize the total traffic load in the network subject to ins...

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Local Search Heuristics for k-Median and Facility Location Problems

Cited by 485 publications

References 6 publications

Clustering under Perturbation Resilience

Clustering under Perturbation Resilience

STFLS: A Heuristic Method for Static and Transportation Facility Location Allocation in Large Spatial Datasets

Content Replication and Delivery in Information‐Centric Networks

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