Optimization problems in multiple subtree graphs

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...

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.

Center location problems on tree graphs with subtree-shaped customers

Fast subtree kernels on graphs

In this article, we propose fast subtree kernels on graphs. On graphs with n nodes and m edges and maximum degree d, these kernels comparing subtrees of height h can be computed in O(mh), whereas the classic subtree kernel by Ramon & Gärtner scales as O(n4h). Key to this efficiency is the observation that the Weisfeiler-Lehman test of isomorphism from graph theory elegantly computes a subtree k...

The Weighted Maximum-Mean Subtree and Other Bicriterion Subtree Problems

We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the problem is trivially solved in linear time. When the objective is the sum of weights that are linear functions of a parameter, we show how to list all optima for ...