Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Linear lists and priority queues as balanced binary trees
Linear lists and priority queues as balanced binary trees
An O(pn2) algorithm for the p -median and related problems on tree graphs
Operations Research Letters
Hierarchical topic segmentation of websites
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Finding the conditional location of a median path on a tree
Information and Computation
Assignment problem in content distribution networks: unsplittable hard-capacitated facility location
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Online clustering with variable sized clusters
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Optimizing server placement in distributed systems in the presence of competition
Journal of Parallel and Distributed Computing
The weighted maximum-mean subtree and other bicriterion subtree problems
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
A new template for solving p-median problems for trees in sub-quadratic time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Assignment problem in content distribution networks: Unsplittable hard-capacitated facility location
ACM Transactions on Algorithms (TALG)
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In the Uncapacitated Facility Location (UFL) problem, there is a fixed cost for opening a facility, and some distance matrix d that determines the cost of distributing commodities from any facility i to any consumer j. The problem is NP-hard in general and when d consists of a distance metric in a graph [7, 12]. However, for the case where the commodity transportation costs are given by path lengths in a tree, an O(n2) dynamic programming algorithm was given by [4, 7]. We improve this dynamic programming algorithm by using the geometry of piecewise linear functions and fast merging of the binary search trees used to store these functions. We achieve the complexity bound of O(n log n) for the Tree Location Problem and some related problems. Our approach gives a general method for solving tree dynamic programming problems.