A polynomial time algorithm to compute the connected tree-width of a series-parallel graph

04/01/2020
by   Christophe Paul, et al.
0

It is well known that the treewidth of a graph G corresponds to the node search number where a team of cops is pursuing a robber that is lazy, visible and has the ability to move at infinite speed via unguarded path. In recent papers, connected node search strategies have been considered. A search stratregy is connected if at each step the set of vertices that is or has been occupied by the team of cops, induced a connected subgraph of G. It has been shown that the connected search number of a graph G can be expressed as the connected treewidth, denoted ctw(G), that is defined as the minimum width of a rooted tree-decomposition ( X,T,r) such that the union of the bags corresponding to the nodes of a path of T containing the root r is connected. Clearly we have that tw(G)≤ctw(G). It is paper, we initiate the algorithmic study of connected treewidth. We design a O(n^2·log n)-time dynamic programming algorithm to compute the connected treewidth of a biconnected series-parallel graphs. At the price of an extra n factor in the running time, our algorithm genralizes to graphs of treewidth at most 2.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/15/2018

Finding small-width connected path decompositions in polynomial time

A connected path decomposition of a simple graph G is a path decompositi...
research
08/28/2023

Faster Min-Cost Flow on Bounded Treewidth Graphs

We present a O(m√(τ)+nτ) time algorithm for finding a minimum-cost flow ...
research
04/24/2020

A linear fixed parameter tractable algorithm for connected pathwidth

The graph parameter of pathwidth can be seen as a measure of the topolog...
research
09/06/2021

Efficient diagonalization of symmetric matrices associated with graphs of small treewidth

Let M=(m_ij) be a symmetric matrix of order n whose elements lie in an a...
research
04/26/2019

The k-path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing

In this paper, we investigate the k-path coloring problem, a variant of ...
research
07/11/2012

PAC-learning bounded tree-width Graphical Models

We show that the class of strongly connected graphical models with treew...
research
06/02/2020

Fast Algorithms for Join Operations on Tree Decompositions

Treewidth is a measure of how tree-like a graph is. It has many importan...

Please sign up or login with your details

Forgot password? Click here to reset