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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Bibliographic Details
Published in:Algorithmica Vol. 68; no. 3; pp. 643 - 670
Main Authors: Gehweiler, Joachim, Lammersen, Christiane, Sohler, Christian
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2014
Springer
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-012-9690-y