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
Handbook of Theoretical Computer Science
Handbook of Theoretical Computer Science
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
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We present O(n3) 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(nc) algorithm (c a constant independent of k) for topological embedding of graphs from subclasses of partial k-trees, as well as an O(n2) 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 nk+O(1) algorithms for solving these problems on arbitrary graphs of pathwidth at most k.