Detecting and Counting Small Pattern Graphs
Author
Summary, in English
We study the induced subgraph isomorphism problem and the general subgraph isomorphism problem for small pattern graphs. We present a new general method for detecting induced subgraphs of a host graph isomorphic to a fixed pattern graph by reduction to polynomial testing for non-identity with zero over a field of finite characteristic. It yields new upper time bounds for several pattern graphs on five vertices and provides an alternative combinatorial method for the majority of pattern graphs on four and three vertices. Since our method avoids the large overhead of fast matrix multiplication, it can be of practical interest even for larger pattern graphs. Next, we derive new upper time bounds on counting the number of isomorphisms between a fixed pattern graph with an independent set of size s and a subgraph of the host graph. We also consider a weighted version of the counting problem, when one counts the number of isomorphisms between the pattern graph and lightest subgraphs, providing a slightly slower combinatorial algorithm.
Publishing year
2013
Language
English
Pages
547-557
Publication/Series
Algorithms and Computation
Volume
8283
Document type
Conference paper
Publisher
Springer
Topic
- Computer Science
- Mathematics
Conference name
24th International Symposium on Algorithms and Computation
Conference date
2013-12-16 - 2013-12-18
Status
Published
ISBN/ISSN/Other
- ISSN: 0302-9743
- ISSN: 1611-3349