Embeddings of k-connected graphs of pathwidth k

Authors:
Arvind Gupta;Naomi Nishimura;Andrzej Proskurowski;Prabhakar Ragde
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, BC, Canada;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada;Department of Computer Science, University of Oregon, Eugene, OR, USA;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada
Venue:
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Year:
2005

Citing 13
Cited 3

Graph algorithms

Handbook of theoretical computer science (vol. A)
On the complexity of finding iso- and other morphisms for partial k-trees

Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
The parallel complexity of tree embedding problems

Journal of Algorithms
Mixed searching and proper-path-width

Theoretical Computer Science
Efficient 2-dimensional approximate matching of half-rectangular figures

Information and Computation
Pathwidth, Bandwidth, and Completion Problems to Proper Interval Graphs with Small Cliques

SIAM Journal on Computing
Efficient and constructive algorithms for the pathwidth and treewidth of graphs

Journal of Algorithms
The complexity of subgraph isomorphism for classes of partial k-trees

Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

SIAM Journal on Computing
Analysis of Algorithms for Listing Equivalence Classes of k-ary Strings

SIAM Journal on Discrete Mathematics
Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees

SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
Graph Theory With Applications

Graph Theory With Applications
Parameterized Complexity

Parameterized Complexity

An exact algorithm for subgraph homeomorphism

Journal of Discrete Algorithms
The space complexity of k-tree isomorphism

ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Log-Space Algorithms for Paths and Matchings in k-Trees

Theory of Computing Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present O(n^3) embedding algorithms (subgraph isomorphism and its generalizations) for classes of graphs of bounded pathwidth, where n is the number of vertices in the graph. These include the first polynomial-time algorithm for minor containment and the first O(n^c) algorithm (c a constant independent of k) for topological embedding of graphs from subclasses of partial k-trees, as well as an O(n^2) algorithm for subgraph isomorphism. Of independent interest are structural properties of k-connected graphs of bounded pathwidth on which our algorithms are based. We also describe special cases which reduce to various generalizations of string matching, permitting more efficient solutions. Finally, we describe n^k^+^O^(^1^) algorithms for solving these problems on arbitrary graphs of pathwidth at most k.