Center location problems on tree graphs with subtree-shaped customers

Center location problems on tree graphs with subtree-shaped customers

Tree-Shaped Facility Location Problems and the Relationship with the Knapsack Problems

The tree-shaped facility location problem aims to locate a subtree on the center of a given tree network. This paper deals with four types of the problems in which the centrality for a subtree is measured by the eccentricity or the distance-sum, and a subtree may contain partial edges or not. We investigate the relationship between these problems and knapsack-type problems. The relation leads t...

Optimization Problems in Multiple Subtree Graphs

We study various optimization problems in t-subtree graphs, the intersection graphs of tsubtrees, where a t-subtree is the union of t disjoint subtrees of some tree. This graph class generalizes both the class of chordal graphs and the class of t-interval graphs, a generalization of interval graphs that has recently been studied from a combinatorial optimization point of view. We present approx...

The p-median and p-center Problems on Bipartite Graphs

Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...

Subtree filament graphs are subtree overlap graphs

We show that the class of intersection graphs of subtree filaments in a tree is identical to the class of overlap graphs of subtrees in a tree.