A Distributed O(1)-Approximation Algorithm for the Uniform Facility Location Problem

We investigate a metric facility location problem in a distributed setting. In this problem, we assume that each point is a client as well as a potential location for a facility and that the opening costs for the facilities and the demands of the clients are uniform. The goal is to open a subset of...

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Veröffentlicht in:	Algorithmica Jg. 68; H. 3; S. 643 - 670
Hauptverfasser:	Gehweiler, Joachim, Lammersen, Christiane, Sohler, Christian
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Boston Springer US 01.03.2014 Springer
Schlagworte:	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer systems and distributed systems. User interface Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Information retrieval. Graph Logistics Mathematics of Computing Operational research and scientific management Operational research. Management science Software Theoretical computing Theory of Computation Facility location Randomized approximation algorithm Synchronous message passing model Distributed algorithm Costs Metric space Distributed system Approximation algorithm Randomized algorithm Modeling Location problem Randomized design Message passing Gossiping(all to all) Metric Graph method Message transmission
ISSN:	0178-4617, 1432-0541
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Abstract	We investigate a metric facility location problem in a distributed setting. In this problem, we assume that each point is a client as well as a potential location for a facility and that the opening costs for the facilities and the demands of the clients are uniform. The goal is to open a subset of the input points as facilities such that the accumulated cost for the whole point set, consisting of the opening costs for the facilities and the connection costs for the clients, is minimized. We present a randomized distributed algorithm that computes in expectation an -approximate solution to the metric facility location problem described above. Our algorithm works in a synchronous message passing model, where each point is an autonomous computational entity that has its own local memory and that communicates with the other entities by message passing. We assume that each entity knows the distance to all the other entities, but does not know any of the other pairwise distances. Our algorithm uses three rounds of all-to-all communication with message sizes bounded to bits, where n is the number of input points. We extend our distributed algorithm to constant powers of metric spaces. For a metric exponent ℓ ≥1, we obtain a randomized -approximation algorithm that uses three rounds of all-to-all communication with message sizes bounded to bits.
AbstractList	We investigate a metric facility location problem in a distributed setting. In this problem, we assume that each point is a client as well as a potential location for a facility and that the opening costs for the facilities and the demands of the clients are uniform. The goal is to open a subset of the input points as facilities such that the accumulated cost for the whole point set, consisting of the opening costs for the facilities and the connection costs for the clients, is minimized. We present a randomized distributed algorithm that computes in expectation an -approximate solution to the metric facility location problem described above. Our algorithm works in a synchronous message passing model, where each point is an autonomous computational entity that has its own local memory and that communicates with the other entities by message passing. We assume that each entity knows the distance to all the other entities, but does not know any of the other pairwise distances. Our algorithm uses three rounds of all-to-all communication with message sizes bounded to bits, where n is the number of input points. We extend our distributed algorithm to constant powers of metric spaces. For a metric exponent ℓ ≥1, we obtain a randomized -approximation algorithm that uses three rounds of all-to-all communication with message sizes bounded to bits.
Author	Sohler, Christian Gehweiler, Joachim Lammersen, Christiane
Author_xml	– sequence: 1 givenname: Joachim surname: Gehweiler fullname: Gehweiler, Joachim organization: Heinz Nixdorf Institute and Computer Science Department, University of Paderborn – sequence: 2 givenname: Christiane surname: Lammersen fullname: Lammersen, Christiane email: christiane.lammersen@tu-dortmund.de organization: School of Computing Science, Simon Fraser University – sequence: 3 givenname: Christian surname: Sohler fullname: Sohler, Christian organization: Department of Computer Science, Technische Universität Dortmund
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Keywords	Facility location Randomized approximation algorithm Synchronous message passing model Distributed algorithm Costs Metric space Distributed system Approximation algorithm Randomized algorithm Modeling Location problem Randomized design Message passing Gossiping(all to all) Metric Graph method Message transmission
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer systems and distributed systems. User interface Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Information retrieval. Graph Logistics Mathematics of Computing Operational research and scientific management Operational research. Management science Software Theoretical computing Theory of Computation
Title	A Distributed O(1)-Approximation Algorithm for the Uniform Facility Location Problem
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