A Dynamic Programming Framework for Combinatorial Optimization Problems on Graphs with Bounded Pathwidth

TL;DR

This paper introduces a dynamic programming framework that efficiently solves certain NP-hard combinatorial optimization problems on graphs with bounded pathwidth, enabling linear-time solutions for network reliability and performance tasks.

Contribution

The paper presents a novel dynamic programming approach tailored for graphs with bounded pathwidth, providing linear-time algorithms for complex network optimization problems.

Findings

Problems are NP-hard in general but solvable in linear time on bounded pathwidth graphs.

Framework improves efficiency for network reliability and fault tolerance assessments.

Applicable to a range of combinatorial optimization problems on specialized graph classes.

Abstract

In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The problems are relevant for assessing network reliability and improving the network's performance and fault tolerance. The main technique considered in this paper is dynamic programming.