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

2015
*
arXiv
*
pre-print

An

arXiv:1503.00617v1
fatcat:6jnwipesxzcavg7teahb36kspa
*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 ...##
###
Efficient Computation of the Characteristic Polynomial of a Threshold Graph
[chapter]

2015
*
Lecture Notes in Computer Science
*

An

doi:10.1007/978-3-319-19647-3_5
fatcat:uil4ypp2qnd6fmw33utxba6ibm
*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 ...##
###
Computing the Characteristic Polynomial of Threshold Graphs

2014
*
Journal of Graph Algorithms and Applications
*

We present an algorithm for constructing

doi:10.7155/jgaa.00342
fatcat:jtwhg3gmtnhnfdvtubtw43vluu
*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*. ...##
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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

2019
*
Machine Learning
*

It has, however,

doi:10.1007/s10994-019-05779-1
fatcat:sx7i2tvwojc2xaufre7vkvthzy
*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). ...##
###
On finding multiplicities of characteristic polynomial factors of black-box matrices

2009
*
Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09
*

We present algorithms and heuristics to

doi:10.1145/1576702.1576723
dblp:conf/issac/DumasPS09
fatcat:52xqw6jjmjernoxvnwrha4jot4
*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*. ...##
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Parametric dictionary learning for graph signals

2013
*
2013 IEEE Global Conference on Signal and Information Processing
*

Experimental results demonstrate

doi:10.1109/globalsip.2013.6736921
dblp:conf/globalsip/ThanouSF13
fatcat:62jymjkuengjvbdfy7fckydbpa
*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. ...##
###
On finding multiplicities of characteristic polynomial factors of black-box matrices
[article]

2009
*
arXiv
*
pre-print

We present algorithms and heuristics to

arXiv:0901.4747v2
fatcat:lb4wngdbbjextbyt2eyzjo5qkq
*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*. ...##
###
Efficient frequent connected subgraph mining in graphs of bounded tree-width

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*...

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

2020
*
arXiv
*
pre-print

We show how

arXiv:2008.01669v1
fatcat:zfjgfjfhprd7basiwznc6jgmka
*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. ...##
###
Efficient Frequent Connected Induced Subgraph Mining in Graphs of Bounded Tree-Width
[chapter]

2013
*
Lecture Notes in Computer Science
*

.,

doi:10.1007/978-3-642-40988-2_40
fatcat:umq45yr3ofectet6kwmwirfk6u
*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*. ...##
###
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

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. ...

##
###
Complexity of coalition structure generation
[article]

2011
*
arXiv
*
pre-print

As

arXiv:1101.1007v6
fatcat:fvnkd3s5hjfffaywumixrlbpw4
*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. ...
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