We investigate the two-median problem on a mesh with M columns and N rows (M ≥ N ), under the Manhattan (L1) metric. We derive exact algorithms with respect to m, n, and r , the number of columns, rows, and vertices, respectively, that contain requests. Specifically, we give an O(mn2 logm) time, O(r ) space algorithm for general (nonuniform) meshes (assuming m≥n). For uniform meshes, we give tw...

The breakpoint median problems arise in the problem of determining phylogenetic history from comparative genome data. We prove that the breakpoint median problems, and a number of related and constrained versions, are all NP-hard.

In this paper we study a facility location problem in the plane in which a single point (median) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the L1 or Manhattan metric. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. ...

The polyhedral structure of the K-median problem on a tree is examined. Even for very small connected graphs, we show that additional constraints are needed to describe the integer polytope. We completely characterize those trees for which an optimal integer LP solution is guaranteed to exist. Also, a new and simpler proof of the worst case bound of an LP solution is provided. We find a new cla...

Structural approaches for pattern recognition frequently make use of graphs to represent objects. The concept of object similarity is of great importance in pattern recognition. The graph edit distance is often used to measure the similarity between two graphs. It basically consists in the amount of distortion needed to transform one graph into the other. The median graph of a set S of graphs i...