The pos/neg-weighted 1-median problem on tree graphs with subtree-shaped customers

Center location problems on tree graphs with subtree-shaped customers

On an Online Spanning Tree Problem in Randomly Weighted Graphs

This paper is devoted to an online variant of the minimum spanning tree problem in randomly weighted graphs. We assume that the input graph is complete and the edge weights are uniform distributed over [0, 1]. An algorithm receives the edges one by one and has to decide immediately whether to include the current edge into the spanning tree or to reject it. The corresponding edge sequence is det...

An Aligned Subtree Kernel for Weighted Graphs

In this paper, we develop a new entropic matching kernel for weighted graphs by aligning depthbased representations. We demonstrate that this kernel can be seen as an aligned subtree kernel that incorporates explicit subtree correspondences, and thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments on standar...

The K-median Problem on a Tree

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...

The median problem on k-partite graphs

In a connected graph G, the status of a vertex is the sum of the distances of that vertex to each of the other vertices in G. The subgraph induced by the vertices of minimum (maximum) status in G is called the median (anti-median) of G. The median problem of graphs is closely related to the optimization problems involving the placement of network servers, the core of the entire networks. Bipart...