Channel assignment on graphs of bounded treewidth

Channel assignment on graphs of bounded treewidth

The following ‘constraint matrix span problem’ arises in the assignment of radio channels in cellular communications systems. Given a graph G with a positive integer length l(xy) for each edge xy, and given a positive integer B, can we assign to each vertex x a channel (x) from 1; : : : ; B such that | (x)− (y)|¿ l(xy) for each edge xy? We show that this problem is NP-complete for graphs of tre...

Recoloring bounded treewidth graphs

Let k be an integer. Two vertex k-colorings of a graph are adjacent if they differ on exactly one vertex. A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. Any graph is (tw + 2)-mixing, where tw is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two (tw + 2)-colorings is a...

On bounded treewidth duality of graphs

Combinatorial Optimization on Graphs of Bounded Treewidth

There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixed-parameter tractable algorithms. Starting from trees and series-parallel graphs, we introduce the concepts of treewidth and tree decompositions, and ill...

Replica Placement on Bounded Treewidth Graphs

We consider the replica placement problem: given a graph with clients and nodes, place replicas on a minimum set of nodes to serve all the clients; each client is associated with a request and maximum distance that it can travel to get served and there is a maximum limit (capacity) on the amount of request a replica can serve. The problem falls under the general framework of capacitated set cov...