• Computational complexity of co...

Treffer: Computational complexity of counting problems on 3-regular planar graphs

Title:
Computational complexity of counting problems on 3-regular planar graphs
Authors:
MINGJI XIA, PENG ZHANG, WENBO ZHAO
Source:
Theory and applications of models of computationTheoretical computer science. 384(1):111-125
Publisher Information:
Amsterdam: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Approximation numérique, Numerical approximation, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Recherche information. Graphe, Information retrieval. Graph, Divers, Miscellaneous, Application, Aplicación, Complexité calcul, Computational complexity, Complejidad computación, Complétude, Completeness, Completitud, Comptage, Counting, Contaje, Condition suffisante, Sufficient condition, Condición suficiente, Graphe planaire, Planar graph, Grafo planario, Graphe régulier, Regular graph, Grafo regular, Informatique théorique, Computer theory, Informática teórica, Interpolation polynomiale, Polynomial interpolation, Interpolación polinomial, Polynôme, Polynomial, Polinomio, Relation récurrence, Recurrence relation, Relación recurrencia, Récurrence, Recurrence, Recurrencia, Variété, Variety, Variedad, Vertex, Vértice, 41A05, 65D05, 68R10, Concordance bipartite, Problème comptage, #P-completeness, Holographic reduction, Matching, Vertex cover
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, P.O. Box 8717, Beijing 100080, China
China Graduate University of Chinese Academy of Sciences, Beijing, China
ISSN:
0304-3975
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=19069685
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.19069685
Database:
PASCAL Archive

Weitere Informationen

A variety of counting problems on 3-regular planar graphs are considered in this paper. We give a sufficient condition which guarantees that the coefficients of a homogeneous polynomial can be uniquely determined by its values on a recurrence sequence. This result enables us to use the polynomial interpolation technique in high dimension to prove the #P-completeness of problems on graphs with special requirements. Using this method, we show that #3-Regular Bipartite Planar Vertex Covers is #P-complete. Furthermore, we use Valiant's Holant Theorem to construct a holographic reduction from it to #2,3-Regular Bipartite Planar Matchings, establishing the #P-completeness of the latter. Finally, we completely classify the problems #Planar Read-twice 3SAT with different ternary symmetric relations according to their computational complexity, by giving several more applications of holographic reduction in proving the #P-completeness of the corresponding counting problems.