A Primal-Dual Approximation Algorithm for the Facility Location Problem with Submodular Penalties

We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 933–942, 2005 ), who presented a 2.50-approximation algorithm that is non-combinatorial because thi...

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Vydáno v:Algorithmica Ročník 63; číslo 1-2; s. 191 - 200
Hlavní autoři: Du, Donglei, Lu, Ruixing, Xu, Dachuan
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer-Verlag 01.06.2012
Springer
Témata:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Flows in networks. Combinatorial problems
Logistics
Mathematical programming
Mathematics of Computing
Operational research and scientific management
Operational research. Management science
Theoretical computing
Theory of Computation
Facility location problem
Approximation algorithm
Submodular function
Geographical isolation
Combinatorial problem
Linear programming
Polynomial method
Combinatorial optimization
Computational complexity
Location problem
Polynomial time
Integer programming
Facility location
Primal dual method
Relaxation method
Ellipsoid
ISSN:0178-4617, 1432-0541
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Popis
Shrnutí:We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 933–942, 2005 ), who presented a 2.50-approximation algorithm that is non-combinatorial because this algorithm has to solve the LP-relaxation of an integer program with exponential number of variables. The only known polynomial algorithm for this exponential LP is via the ellipsoid algorithm as the corresponding separation problem for its dual program can be solved in polynomial time. By exploring the properties of the submodular function, we offer a primal-dual 3-approximation combinatorial algorithm for this problem.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-011-9526-1