Proceedings ArticleDOI
Isomorphism of graphs with bounded eigenvalue multiplicity
László Babai,D. Yu. Grigoryev,David M. Mount +2 more
- pp 310-324
TLDR
Two polynomial time algorithms are described which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity, if X and Y are graphs of eigenvalue multiplicity m.Abstract:
We investigate the connection between the spectrum of a graph, i.e. the eigenvalues of the adjacency matrix, and the complexity of testing isomorphism. In particular we describe two polynomial time algorithms which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity. If X and Y are graphs of eigenvalue multiplicity m, then the isomorphism of X and Y can be tested by an O(n4m+c) deterministic and by an O(n2m+c) Las Vegas algorithm, where n is the number of vertices of X and Y.read more
Citations
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Journal ArticleDOI
The QAP-polytope and the graph isomorphism problem
Pawan Aurora,Shashank K. Mehta +1 more
TL;DR: A geometric approach to solve the Graph Isomorphism (GI in short) problem and defines a partial ordering on each exponential sized family of facet defining inequalities and shows that if there exists a common minimal violated inequality for all points in the feasible region outside the QAP-polytope, then the problem can be solved in polynomial time.
Fixed-parameter tractability of the graph isomorphism and canonization problems
TL;DR: This thesis aims to provide a survey of the graph isomorphism and canonization problems in the context of fixed-parameter tractability and to look at the asymptotic runtime differences between graph isomorphicism and graph canonization (if there are any).
Title of dissertation: COMPUTATIONALLY COMPARING BIOLOGICAL NETWORKS AND RECONSTRUCTING THEIR EVOLUTION
Rob Patro,Carl Kingsford +1 more
TL;DR: GrowCode as discussed by the authors is based on an ensemble of support vector machines and exhibits state-of-the-art performance on the 2010 DREAM5 competition. But it is not suitable for the analysis of biological networks.
Posted Content
Seeded Graph Matching via Large Neighborhood Statistics
Elchanan Mossel,Jiaming Xu +1 more
TL;DR: Barak et al. as discussed by the authors showed that the information-theoretic limit of graph sparsity can be achieved in time polynomial in the number of vertices in the graph.
Journal ArticleDOI
Applications of dimensionality reduction and exponential sums to graph automorphism
TL;DR: It is shown that orthogonal projections of the simplex onto a lower dimensional space preserves an automorphism if and only if the space is an invariant subspace of the Automorphism.
References
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MonographDOI
Algebraic graph theory
TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.
Book
Spectra of graphs : theory and application
TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.
Proceedings ArticleDOI
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
John E. Hopcroft,J. K. Wong +1 more
TL;DR: The time bound for planar graph isomorphism is improved to O(|V|) time and the algorithm can be easily extended to partition a set of planar graphs into equivalence classes of isomorphic graphs in time linear in the total number of vertices in all graphs in the set.