Finite dominating sets for network location problems
Operations Research
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Reliability Models for Facility Location: The Expected Failure Cost Case
Transportation Science
Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Locating Servers for Reliability and Affine Embeddings
SIAM Journal on Discrete Mathematics
A faster PSPACE algorithm for deciding the existential theory of the reals
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Extensive facility location problems on networks with equity measures
Discrete Applied Mathematics
The continuous and discrete path-variance problems on trees
Networks - Special Issue on Trees
Reliable Facility Location Design Under the Risk of Disruptions
Operations Research
The multi-facility median problem with Pos/Neg weights on general graphs
Computers and Operations Research
The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms
INFORMS Journal on Computing
On the exponential cardinality of FDS for the ordered p-median problem
Operations Research Letters
Algorithmic results for ordered median problems
Operations Research Letters
Range minimization problems in path-facility location on trees
Discrete Applied Mathematics
Algorithms in Combinatorial Geometry
Algorithms in Combinatorial Geometry
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In this paper we study facility location problems on graphs under the most common optimization criteria, such as, median, center and centdian, but we incorporate in the objective function some reliability aspects. Assuming that facilities may become unavailable with a certain probability, the problem consists of locating facilities minimizing the overall or the maximum expected service cost in the long run, or a convex combination of the two. We show that the k-facility problem on general networks is NP-hard. Then, we provide efficient algorithms for these problems for the cases of k=1,2, both on general networks and on trees. We also explain how our methodology extends to handle a more general class of unreliable point facility location problems related to the ordered median objective function.