Paper Info
Title
Experimental Evaluation of a Branch-and-Bound Algorithm for Computing Pathwidth and Directed Pathwidth
Abstract
Path decompositions of graphs are an important ingredient of dynamic programming algorithms for solving efficiently many NP-hard problems. Therefore, computing the pathwidth and associated path decomposition of graphs has both a theoretical and practical interest. In this article, we design a branch-and-bound algorithm that computes the exact pathwidth of graphs and a corresponding path decomposition. Our main contribution consists of several nontrivial techniques to reduce the size of the input graph (preprocessing) and to cut the exploration space during the search phase of the algorithm. We evaluate experimentally our algorithm by comparing it to existing algorithms of the literature. It appears from the simulations that our algorithm offers a significant gain with respect to previous work. In particular, it is able to compute the exact pathwidth of any graph with less than 60 nodes in a reasonable running time (≤ 10min on a standard laptop). Moreover, our algorithm achieves good performance when used as a heuristic (i.e., when returning best result found within bounded time limit). Our algorithm is not restricted to undirected graphs since it actually computes the directed pathwidth that generalizes the notion of pathwidth to digraphs.
Year
DOI
Venue
2016
10.1145/2851494
Journal of Experimental Algorithmics
Keywords
Field
DocType
Graph,branch-and-bound,directed pathwidth,pathwidth,vertex separation
Discrete mathematics,Dynamic programming,Mathematical optimization,Heuristic,Branch and bound,Preprocessor,Time limit,Graph bandwidth,Pathwidth,Mathematics,Bounded function
Journal
Volume
Issue
ISSN
21
1
1084-6654
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
David Coudert100.34
Dorian Mazauric28213.34
Nicolas Nisse331332.82