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Efficient Computation of the Characteristic Polynomial of a Threshold Graph [article]

Martin Fürer
2015 arXiv   pre-print
An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph.  ...  Keywords: Efficient Algorithms, Threshold Graphs, Characteristic Polynomial.  ...  Computation of the Characteristic Polynomial of a Threshold Graph The adjacency matrix A of the n-vertex threshold graph G defined by the sequence (b 1 , . . . , b n−1 ) is the matrix M 0 0...0 b 1 b 2  ... 
arXiv:1503.00617v1 fatcat:6jnwipesxzcavg7teahb36kspa

Efficient Computation of the Characteristic Polynomial of a Threshold Graph [chapter]

Martin Fürer
2015 Lecture Notes in Computer Science  
An efficient algorithm is presented to compute the characteristic polynomial of a threshold graph.  ...  We obtain a running time of O(n log 2 n) for computing the characteristic polynomial, while the previously fastest algorithm ran in quadratic time.  ...  Computation of the Characteristic Polynomial of a Threshold Graph The adjacency matrix A of the n-vertex threshold graph G defined by the sequence (b 1 , . . . , b n−1 ) is the matrix M 0 0...0 b 1 b 2  ... 
doi:10.1007/978-3-319-19647-3_5 fatcat:uil4ypp2qnd6fmw33utxba6ibm

Computing the Characteristic Polynomial of Threshold Graphs

David P. Jacobs, Vilmar Trevisan, Fernando Tura
2014 Journal of Graph Algorithms and Applications  
We present an algorithm for constructing the characteristic polynomial of a threshold graph's adjacency matrix. The algorithm is based on a diagonalization procedure that is easy to describe.  ...  Fernando Tura acknowledges the support of CAPES Grant 0283/12-6.  ...  The method described in this paper is an efficient algorithm that can compute the characteristic polynomial of any threshold graph.  ... 
doi:10.7155/jgaa.00342 fatcat:jtwhg3gmtnhnfdvtubtw43vluu

Page 6056 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
On the other hand, we describe a new polynomially solvable case for the problem in bi- partite graphs which deals with a generalization of bi-complement reducible graphs.”  ...  It is noted also that the Horn envelope of £ can be computed in polynomial time in the representation (ii), while the size of a CNF for the Horn envelope can be exponential in the size of CNFs of &; (i  ... 

Probabilistic and exact frequent subtree mining in graphs beyond forests

Pascal Welke, Tamás Horváth, Stefan Wrobel
2019 Machine Learning  
It has, however, the drawback that the number of sampled spanning trees must be bounded by a polynomial of the size of the transaction graphs, resulting in less impressive recall even for slightly more  ...  We demonstrate the superiority of our algorithm over the simple one on threshold graphs used e.g. in spectral clustering.  ...  Acknowledgements Part of this work has been funded by the Ministry of Education and Research of Germany (BMBF) under project ML2R (grant number 01/S18038C).  ... 
doi:10.1007/s10994-019-05779-1 fatcat:sx7i2tvwojc2xaufre7vkvthzy

On finding multiplicities of characteristic polynomial factors of black-box matrices

Jean-Guillaume Dumas, Clément Pernet, B. David Saunders
2009 Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09  
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial.  ...  The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to matrices either over the integers or over a large enough finite field.  ...  We helped Royle to investigate further the computation of the characteristic polynomial of the symmetric cubes of strongly regular graphs.  ... 
doi:10.1145/1576702.1576723 dblp:conf/issac/DumasPS09 fatcat:52xqw6jjmjernoxvnwrha4jot4

Parametric dictionary learning for graph signals

Dorina Thanou, David I Shuman, Pascal Frossard
2013 2013 IEEE Global Conference on Signal and Information Processing  
Experimental results demonstrate the efficiency of the proposed algorithm for the sparse approximation of graph signals.  ...  We incorporate the graph structure by forcing the learned dictionaries to be concatenations of subdictionaries that are polynomials of the graph Laplacian matrix.  ...  ACKNOWLEDGEMENT The authors would like to thank Xiaowen Dong for the fruitful discussions and for providing the Flickr data.  ... 
doi:10.1109/globalsip.2013.6736921 dblp:conf/globalsip/ThanouSF13 fatcat:62jymjkuengjvbdfy7fckydbpa

On finding multiplicities of characteristic polynomial factors of black-box matrices [article]

Jean-Guillaume Dumas, Clément Pernet (INRIA Rhône-Alpes / LIG Laboratoire d'Informatique de Grenoble), B. David Saunders
2009 arXiv   pre-print
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial.  ...  The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to matrices either over the integers or over a large enough finite field.  ...  We helped Royle to investigate further the computation of the characteristic polynomial of the symmetric cubes of strongly regular graphs.  ... 
arXiv:0901.4747v2 fatcat:lb4wngdbbjextbyt2eyzjo5qkq

Efficient frequent connected subgraph mining in graphs of bounded tree-width

Tamás Horváth, Jan Ramon
2010 Theoretical Computer Science  
The frequent connected subgraph mining problem, i.e., the problem of listing all connected graphs that are subgraph isomorphic to at least a certain number of transaction graphs of a database, cannot be  ...  Since subgraph isomorphism remains NP-complete for bounded tree-width graphs, the positive complexity result of this paper shows that efficient frequent pattern mining is possible even for computationally  ...  In a nutshell, the main result of [17] is that several graph morphisms, including subgraph isomorphism, can be decided efficiently by a dynamic programming algorithm computing a certain set of polynomially  ... 
doi:10.1016/j.tcs.2010.03.030 fatcat:b7g2qgz3znhmhhcneyeitgzoqa

Eigenvalues of graph Laplacians via rank-one perturbations [article]

Steven Klee, Matthew T. Stamps
2020 arXiv   pre-print
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation.  ...  We apply our finding to give new short proofs of the spectral version of Kirchhoff's Matrix Tree Theorem and known derivations for the characteristic polynomials of the Laplacians for several well known  ...  Acknowledgments We are grateful to Mohamed Omar for helpful and encouraging conversations during the early stages of this project.  ... 
arXiv:2008.01669v1 fatcat:zfjgfjfhprd7basiwznc6jgmka

Efficient Frequent Connected Induced Subgraph Mining in Graphs of Bounded Tree-Width [chapter]

Tamás Horváth, Keisuke Otaki, Jan Ramon
2013 Lecture Notes in Computer Science  
., the problem of listing all connected graphs that are induced subgraph isomorphic to at least a certain number of transaction graphs.  ...  Since induced subgraph isomorphism between bounded tree-width graphs is NP-complete, the positive result of this paper provides another example of efficient pattern mining with respect to computationally  ...  By setting the frequency threshold t to 1, our main result implies that one can efficiently generate all distinct connected induced subgraphs of a bounded tree-width graph.  ... 
doi:10.1007/978-3-642-40988-2_40 fatcat:umq45yr3ofectet6kwmwirfk6u

Page 8250 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
H. (1-DUKE-C; Durham, NC) Efficient parallel computation of the characteristic polynomial of a sparse, separable matrix. (English summary) Algorithmica 29 (2001), no. 3, 487-510.  ...  This paper gives a parallel algorithm for exact computation of the characteristic polynomial of a sparse symmetric matrix with parallel time O((In())? * (In(s()))?)  ... 

Page 7667 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
Therein, the properties of circuits, whose processing units compute linear threshold functions—threshold circuits, are analysed and the complexity classes of problems re- quiring threshold circuits having  ...  Summary: “Identification by algorithmic devices of programs for computable functions from their graphs is a well studied problem in learning theory.  ... 

ProMotE: an efficient algorithm for counting independent motifs in uncertain network topologies

Yuanfang Ren, Aisharjya Sarkar, Tamer Kahveci
2018 BMC Bioinformatics  
The fact that biological interactions are uncertain events further complicates the problem, as it makes the existence of an embedding of a given motif an uncertain event as well.  ...  We utilize a polynomial model to capture the uncertainty. We develop three strategies to scale our algorithm to large networks.  ...  Neither funding body played any role in the design of this study and collection, analysis, and interpretation of data or in writing the manuscript.  ... 
doi:10.1186/s12859-018-2236-9 pmid:29940838 pmcid:PMC6020255 fatcat:4jk22q752vharoeogri3w42fse

Complexity of coalition structure generation [article]

Haris Aziz, Bart de Keijzer
2011 arXiv   pre-print
As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number  ...  One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant  ...  Acknowledgements We thank Hans Georg Seedig and the anonymous referees for helpful feedback.  ... 
arXiv:1101.1007v6 fatcat:fvnkd3s5hjfffaywumixrlbpw4
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