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Exact exponential-time algorithms for finding bicliques

2010
*
Information Processing Letters
*

*In*this paper, we design

*a*polynomial-space O(1.6914 n )

*time*

*algorithm*

*for*this problem. It is based on an

*algorithm*

*for*bipartite

*graphs*that runs

*in*

*time*O(1.30052 n ). ... Due to

*a*large number of applications,

*bicliques*of

*graphs*have been widely considered

*in*the literature. This paper focuses on non-induced

*bicliques*. ... We already mentioned that CBVC, the parameterized dual of Non-induced (k 1 , k 2 )

*Biclique*, is

*in*FPT. It is

*a*natural question to ask whether Non-induced (k 1 , k 2 )

*Biclique*is

*in*FPT as well. ...

##
###
An exact exponential time algorithm for counting bipartite cliques

2012
*
Information Processing Letters
*

We present

doi:10.1016/j.ipl.2012.04.001
fatcat:yol6ix5pcrcubojgoxekfxkfja
*a*simple*exact**algorithm**for*counting*bicliques*of given size*in**a*bipartite*graph*on n vertices. ... We achieve running*time*of O(1.2491 n ), improving upon known*exact**algorithms**for**finding*and counting bipartite cliques. ... Acknowledgements The author would like to thank two anonymous referees*for*many helpful comments and suggestions and Nina Taslaman*for*discussions on*graph*theory terminology. ...##
###
Cartesian contour

2009
*
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '09
*

We develop

doi:10.1145/1557019.1557069
dblp:conf/kdd/JinXL09
fatcat:bpt55h3qazbmjgwung5stkqskq
*a*novel approach utilizing the technique developed*in*frequent itemset mining, set cover, and max k-cover to approximate the minimal*biclique*set cover problem. ... We perform*a*theoretical investigation of the concise representation problem and link it to the*biclique*set cover problem and prove its NP-hardness. ...*Finding*Low Price Sub-*biclique*from*Biclique**in*Polynomial*Time**In*this subsection, we introduce*a*fundamental lemma and*algorithm*to identify*a*sub-*biclique*with cheapest price. ...##
###
Obtaining Maximal Concatenated Phylogenetic Data Sets from Large Sequence Databases

2003
*
Molecular biology and evolution
*

We developed an

doi:10.1093/molbev/msg115
pmid:12777519
fatcat:j3bx2qsenbhzxnrdr3r4ef2jdy
*exact**algorithm**for*obtaining the largest multigene data sets from*a*collection of sequences. ... However, the skewed distribution of sequences*in*these databases permits all such data sets to be obtained*in*reasonable computing*times*even*for*large numbers of sequences. ... We thank two anonymous reviewers*for*comments. ...##
###
On Independent Sets and Bicliques in Graphs
[chapter]

2008
*
Lecture Notes in Computer Science
*

Our major contribution is an

doi:10.1007/978-3-540-92248-3_16
fatcat:wlzqjssmzfadzmhhk3grlih6oa
*exact**exponential*-*time**algorithm*. ... This branching*algorithm*computes the number of distinct maximal independent sets*in**a**graph**in**time*O(1.3642 n ), where n is the number of vertices of the input*graph*. ... Acknowledgment The authors would like to thank the coordinating editor, Richard Cole,*for*his suggestion how to improve the upper bound of Theorem 3 from n · 3 n/3 to 1 3 1/3 −1 · 3 n/3 . ...##
###
On Independent Sets and Bicliques in Graphs

2010
*
Algorithmica
*

Our major contribution is an

doi:10.1007/s00453-010-9474-1
fatcat:mfks63jsivgf3j5waurcs7klt4
*exact**exponential*-*time**algorithm*. ... This branching*algorithm*computes the number of distinct maximal independent sets*in**a**graph**in**time*O(1.3642 n ), where n is the number of vertices of the input*graph*. ... Acknowledgment The authors would like to thank the coordinating editor, Richard Cole,*for*his suggestion how to improve the upper bound of Theorem 3 from n · 3 n/3 to 1 3 1/3 −1 · 3 n/3 . ...##
###
Scale Reduction Techniques for Computing Maximum Induced Bicliques

2017
*
Algorithms
*

*biclique*[5] and maximum balanced

*bicliques*[19] to

*exact*,

*exponential*-

*time*methods [20], approximation

*algorithms*[21] and mining quasi-

*bicliques*[22, 23] . ... aiming to

*find*

*a*

*biclique*with the maximum number of edges

*in*the

*graph*. ... No funds were received

*for*covering the costs to publish

*in*open access. ...

##
###
Scalable Large Near-Clique Detection in Large-Scale Networks via Sampling

2015
*
Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15
*

We also extend this family of formulations to bipartite

doi:10.1145/2783258.2783385
dblp:conf/kdd/MitzenmacherPPT15
fatcat:gmn7sydbezhx3etolrwjameehu
*graphs*by introducing the (p, q)-*biclique*densest subgraph problem ((p,q)-*Biclique*-DSP), and devise an*exact**algorithm*that can treat both clique ... and*biclique*densities*in**a*unified way. ... Acknowledgments Michael Mitzenmacher was supported*in*part by NSF grants IIS-0964473, CNS-1228598, and CCF-1320231. Jakub Pachocki and Shen Chen Xu were supported*in*part by NSF grant CCF-1065106. ...##
###
Detecting Bicliques in GF[q]
[chapter]

2013
*
Lecture Notes in Computer Science
*

We consider the problem of

doi:10.1007/978-3-642-40988-2_33
fatcat:kopoglsadbhdtolo7ndnfcdvs4
*finding*planted*bicliques**in*random matrices over GF [q]. That is, our input matrix is*a*GF [q]-sum of an unknown*biclique*(rank-1 matrix) and*a*random matrix. ... We study different models*for*the random*graphs*and characterize the conditions when the planted*biclique*can be recovered. ... Lemma 9, and Eq. 14,*in*the Appendix. 4 Related Work*Finding*large*bicliques*has seen*a*lot of attention. Most research aims at*finding**exact**bicliques*, that is, complete bipartite subgraphs. ...##
###
Fast exact and heuristic methods for role minimization problems

2008
*
Proceedings of the 13th ACM symposium on Access control models and technologies - SACMAT '08
*

*For*our test cases, these reductions either solve the problem, or reduce the problem enough that we

*find*the optimum solution with

*a*(worstcase)

*exponential*method. ... We introduce fast

*graph*reductions that allow recovery of the solution from the solution to

*a*problem on

*a*smaller input

*graph*. ... Acknowledgement We thank Mehul Shah

*for*very helpful discussions on technical content, and the referees, who provided excellent suggestions as to its presentation. ...

##
###
Optimizing adiabatic quantum program compilation using a graph-theoretic framework

2018
*
Quantum Information Processing
*

To address these barriers, we introduce

doi:10.1007/s11128-018-1863-4
fatcat:yczohpipyzczbdwq7ptiyfrbhy
*a**graph*-theoretic framework*for*developing structured embedding*algorithms*. ... Additionally, while*finding**a*single embedding is difficult, no generalized method is known*for*tuning embeddings to use minimal hardware resources. ... Acknowledgements The authors would like to thank Steve Reinhardt and the anonymous two reviewers*for*feedback. ...##
###
On the Phase Transition of Finding a Biclique in a larger Bipartite Graph
[article]

2016
*
arXiv
*
pre-print

We report on the phase transition of

arXiv:1609.05876v1
fatcat:ivnkhqa76re5bmuzmdy4y3l5yy
*finding**a*complete subgraph, of specified dimensions,*in**a*bipartite*graph*. ...*Finding**a*complete subgraph*in**a*bipartite*graph*is*a*problem that has growing attention*in*several domains, including bioinformatics, social network analysis and domain clustering. ...*In*conclusion, there is an*exponential*growth*in*the number of combina- Figure 9 : 9 Percentile 90%, 25% and median cost of*finding**a**biclique*with size z = 8 and maximal weight*for**a*number of observations ...##
###
An Exact Branch and Bound Algorithm with Symmetry Breaking for the Maximum Balanced Induced Biclique Problem
[chapter]

2014
*
Lecture Notes in Computer Science
*

We show how techniques from state-of-the-art branch and bound

doi:10.1007/978-3-319-07046-9_16
fatcat:ospxjhttr5gxtkgw7oy3iyhddi
*algorithms**for*the maximum clique problem can be adapted to solve the maximum balanced induced*biclique*problem. ... Finally, we discuss one particular class of*graphs*where the algorithm's bound is ineffective, and show how to detect this situation and fall back to*a*simpler but faster*algorithm*. ... degrees, indirect colouring, or the fact that*finding*an (unbalanced) induced*biclique**in**a*bipartite*graph*can be done*in*polynomial*time*via*a*matching*algorithm*. ...##
###
Phase Transition in Matched Formulas and a Heuristic for Biclique Satisfiability
[article]

2018
*
arXiv
*
pre-print

*In*this paper we describe

*a*heuristic

*algorithm*

*for*recognizing whether

*a*formula is

*biclique*satisfiable and we evaluate it by experiments on random formulas. ...

*A*formula is

*biclique*satisfiable if its incidence

*graph*admits covering by pairwise disjoint bounded

*bicliques*. Recognizing if

*a*formula is

*biclique*satisfiable is NP-complete. ...

*In*this section we shall describe

*a*heuristic

*algorithm*

*for*

*finding*

*a*bounded

*biclique*cover. ...

##
###
Optimizing Adiabatic Quantum Program Compilation using a Graph-Theoretic Framework
[article]

2017
*
arXiv
*
pre-print

To address these barriers, we introduce

arXiv:1704.01996v2
fatcat:55xateudzff4lpudukl5rdxjq4
*a**graph*-theoretic framework*for*developing structured embedding*algorithms*. ... Additionally, while*finding**a*single embedding is difficult, no generalized method is known*for*tuning embeddings to use minimal hardware resources. ... However, this implies*a*small OCT set, therefore the*exact**algorithm*will have an*exponentially*faster run*time*. Therefore approximating MaxBipartite makes more sense*in*this context. ...
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