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Counting the Number of Perfect Matchings, and Generalized Decision Trees.
- Source :
-
Problems of Information Transmission . Apr2021, Vol. 57 Issue 2, p143-160. 18p. - Publication Year :
- 2021
-
Abstract
- We consider a generalization of the Pólya–Kasteleyn approach to counting the number of perfect matchings in a graph based on computing the symbolic Pfaffian of a directed adjacency matrix of the graph. Complexity of algorithms based on this approach is related to the complexity of the sign function of a perfect matching in generalized decision tree models. We obtain lower bounds on the complexity of the sign of a perfect matching in terms of the deterministic communication complexity of the XOR sign function of a matching. These bounds demonstrate limitations of the symbolic Pfaffian method for both the general case and the case of sparse graphs. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DECISION trees
*SPARSE graphs
*COUNTING
*ALGORITHMS
*GENERALIZATION
Subjects
Details
- Language :
- English
- ISSN :
- 00329460
- Volume :
- 57
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Problems of Information Transmission
- Publication Type :
- Academic Journal
- Accession number :
- 151291681
- Full Text :
- https://doi.org/10.1134/S0032946021020046