An O(n) algorithm for the linear multiple choice knapsack problem and related problems
Information Processing Letters
Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
On the Power of Discrete and of Lexicographic Helly-Type Theorems
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
An optimal algorithm for the continuous/discrete weighted 2-center problem in trees
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Improved complexity bounds for location problems on the real line
Operations Research Letters
Optimal geometric partitions, covers and K-centers
MCBE'08 Proceedings of the 9th WSEAS International Conference on Mathematics & Computers In Business and Economics
Efficient algorithms for the weighted k-center problem on a real line
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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An optimal linear time algorithm for the unweighted p-center problems in trees has been known since 1991 [4]. No such worst-case linear time result is known for the weighted version of the p-center problems, even for a path graph. In this paper, for fixed p, we propose two lineartime algorithms for the weighted p-center problem for points on the real line, thereby partially resolving a long-standing open problem. One of our approaches generalizes the trimming technique of Megiddo [10], and the other one is based on the parametric pruning technique, introduced here. The proposed solutions make use of the solutions of another variant of the center problem called the conditional center location problem [13].