On a multidimensional search technique and its application to the Euclidean one centre problem
SIAM Journal on Computing
A linear-time algorithm for concave one-dimensional dynamic programming
Information Processing Letters
Algebraic optimization: the Fermat-Weber location problem
Mathematical Programming: Series A and B
Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Optimal partitioning of sequences
Journal of Algorithms
Placing resources on a growing line
Journal of Algorithms
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Computing a minimum weight k-link path in graphs with the concave Monge property
Journal of Algorithms - Special issue on SODA '95 papers
Efficient Partitioning of Sequences
IEEE Transactions on Computers
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A Simple Linear Time Algorithm for Concave One-Dimensional Dynamic Programming
A Simple Linear Time Algorithm for Concave One-Dimensional Dynamic Programming
Minimum Lk path partitioning-An illustration of the Monge property
Operations Research Letters
Monge strikes again: optimal placement of web proxies in the internet
Operations Research Letters
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We study the one-dimensional facility location problems. Given a set of n customers on the real line, each customer having a cost for setting up a facility at its position, and an integer k, we seek to find at most k of the customers to set up facilities for serving all n customers such that the total cost for facility set-up and service transportation is minimized. We consider several problem variations including k-median and k-coverage and a linear model. We also study a related path equipartition problem: Given a vertex-weighted path and an integer k, remove k-1 edges so that the weights of the resulting k sub-paths are as equal as possible. Based on new problem modeling and observations, we present improved algorithms for these problems over the previous work.