e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for geometric median problems
Information Processing Letters
New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An 0.828–approximation algorithm for the uncapacitated facility location problem
Discrete Applied Mathematics
A 3-approximation algorithm for the k-level uncapacitated facility location problem
Information Processing Letters
Approximating the two-level facility location problem via a quasi-greedy approach
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A review of hierarchical facility location models
Computers and Operations Research
New facets for the two-stage uncapacitated facility location polytope
Computational Optimization and Applications
Tabu based heuristics for the generalized hierarchical covering location problem
Computers and Industrial Engineering
Computers and Operations Research
A note on the maximization version of the multi-level facility location problem
Operations Research Letters
Computers and Industrial Engineering
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We consider the maximization version of the two level uncapacitated facility location problem, in the following formulation:maxS"1xS"2@?FxEC(S"1,S"2)=maxS"1xS"2@?FxE@?k@?Dmax(i,j)@?S"1xS"2c"i"j"k-@?i@?S"1f"i-@?j@?S"2e"j,where F,E are finite sets and c"i"j"k,f"i,e"j=0 are real numbers. Denote by C^* the optimal value of the problem and by C"R=@?"k"@?"Dmin"("i","j")"@?"F"x"Ec"i"j"k-@?"i"@?"Ff"i-@?"j"@?"Ee"j. We present a polynomial time algorithm based on randomized rounding that finds a solution (S"1,S"2) such thatC(S"1,S"2)-C"R=0.47(C^*-C"R).