Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Analysis of a local search heuristic for facility location problems
Journal of Algorithms
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Information Processing Letters
Facility Location with Nonuniform Hard Capacities
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Improved approximation algorithms for capacitated facility location problems
Mathematical Programming: Series A and B
A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem
Mathematics of Operations Research
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
Covering Problems with Hard Capacities
SIAM Journal on Computing
An improved approximation algorithm for vertex cover with hard capacities
Journal of Computer and System Sciences
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We consider a generalization of the well-known domination problem on graphs. The (soft) capacitated domination problem with demand constraints is to find a dominating set D of minimum cardinality satisfying both the capacity and demand constraints. The capacity constraint specifies that each vertex has a capacity that it can use to meet the demand of dominated vertices in its closed neighborhood, and the number of copies of each vertex allowed in D is unbounded. The demand constraint specifies that the demand of each vertex in V is met by the capacities of vertices in D dominating it. In this paper, we study the capacitated domination problem on trees. We present a linear time algorithm for the unsplittable demand model, and a pseudo-polynomial time algorithm for the splittable demand model. In addition, we show that the capacitated domination problem on trees with splittable demand constraints is NP-complete (even for its integer version) and provide a 3/2-approximation algorithm. We also give a primal-dual approximation algorithm for the weighted capacitated domination problem with splittable demand constraints on general graphs.