Complexity of robust single facility location problems on networks with uncertain edge lengths
Discrete Applied Mathematics
The Minmax Relative Regret Median Problem on Networks
INFORMS Journal on Computing
Improved algorithms for the minmax-regret 1-center and 1-median problems
ACM Transactions on Algorithms (TALG)
Minimax Regret Single-Facility Ordered Median Location Problems on Networks
INFORMS Journal on Computing
Improved algorithms for the minmax regret 1-median problem
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Improved algorithms for the minmax-regret 1-center problem
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Broadcasting in heterogeneous tree networks with uncertainty
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
An O(nlogn) version of the Averbakh-Berman algorithm for the robust median of a tree
Operations Research Letters
Facility location problems with uncertainty on the plane
Discrete Optimization
Minmax regret solutions for minimax optimization problems with uncertainty
Operations Research Letters
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We consider the 1-median problem on a network with uncertain weights of nodes. Specifically, for each node, only an interval estimate of its weight is known. It is required to find the "minimax regret" location, i.e., to minimize the worst-case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place. We present the first polynomial algorithm for this problem on a general network. For the problem on a tree network, we discuss an algorithm with an order of complexity improved over the algorithms known in the literature.