Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Algorithms for a core and k-tree core of a tree
Journal of Algorithms
On the conditional p-median problem
Computers and Operations Research
Efficient algorithms for finding a core of a tree with a specified length
Journal of Algorithms
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Discrete Applied Mathematics
Algorithms for path medi-centers of a tree
Computers and Operations Research - location science
The Centdian subtree on tree networks
Discrete Applied Mathematics
Finding a 2-Core of a Tree in Linear Time
SIAM Journal on Discrete Mathematics
Finding Cores of Limited Length
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Finding the conditional location of a median path on a tree
Information and Computation
Extensive facility location problems on networks with equity measures
Discrete Applied Mathematics
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In this paper we deal with the location of extensive facilities on trees, both discrete and continuous, under the condition that existing facilities are already located. We require that the selected new server is a subtree, although we also specialize to the case of paths. We study the problem with the two most widely used criteria in Location Analysis: center and median. Our main results under the center criterion are nestedness properties of the solution and subquadratic algorithms for the location of paths and subtrees. For the case of the median criterion we prove that unlike the case where there is no existing facility, the continuous conditional median subtree problem is NP-hard and we develop a corresponding fully polynomial approximation algorithm. We also present subquadratic algorithms for almost all other models.