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Lecture Notes in Computer Science
In this paper we consider the problem of locating path-shaped or tree-shaped (extensive) facility in trees under the conditions that exisiting facilities are already located. We introduced a parametric-pruning method to solve the weighted 1-center problem in trees. This method is more general than the method proposed by Megiddo in  . Using this method, optimal algorithms are devised for solving the conditional extensive weighted 1-center location problem in trees. This improves the recent results of O(n log n) by Tamir et al.  .doi:10.1007/11940128_39 fatcat:5zaeqycs6vcjbjwxuput3oykmq