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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 )

doi:10.1016/j.ipl.2010.10.020
fatcat:auug2gskdfelrpykz5mrvyswwm
*time**algorithm**for*this problem. It is based on an*algorithm**for*bipartite graphs that runs in*time*O(1.30052 n ). ... The NP-complete problem of*finding*a non-induced (k 1 , k 2 )-*biclique*asks to decide whether G contains a non-induced*biclique*(X, Y ) such that |X| = k 1 and |Y | = k 2 . ... 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. ...##
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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. ...##
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An exact exponential time algorithm for counting bipartite cliques

2012
*
Information Processing Letters
*

We achieve running

doi:10.1016/j.ipl.2012.04.001
fatcat:yol6ix5pcrcubojgoxekfxkfja
*time*of O(1.2491 n ), improving upon known*exact**algorithms**for**finding*and counting bipartite cliques. ... We present a simple*exact**algorithm**for*counting*bicliques*of given size in a bipartite graph on n vertices. ... 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. ...##
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Cartesian contour

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

We perform a theoretical investigation of the concise representation problem and link it to the

doi:10.1145/1557019.1557069
dblp:conf/kdd/JinXL09
fatcat:bpt55h3qazbmjgwung5stkqskq
*biclique*set cover problem and prove its NP-hardness. ... We develop 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. ... Thus, the overall running*time**for*the minimal*biclique*set cover problem includes the*time*of running the frequent itemsets mining*algorithm*, which we do not consider*for*the*time*complexity analysis ...##
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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*. ... We use this counting*algorithm*and previously known*algorithms**for*various other problems related to independent sets to derive*algorithms**for*problems related to*bicliques*via polynomial-*time*reductions ... 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 . ...##
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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*. ... We use this counting*algorithm*and previously known*algorithms**for*various other problems related to independent sets to derive*algorithms**for*problems related to*bicliques*via polynomial-*time*reductions ... 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 . ...##
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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] . ... Different

*algorithms*have been proposed

*for*

*biclique*community detection ranging from enumeration of all maximal (non-induced)

*bicliques*of a graph [13, [15] [16] [17] [18] ,

*finding*a maximum edge cardinality ... No funds were received

*for*covering the costs to publish in open access. ...

##
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Detecting Bicliques in GF[q]
[chapter]

2013
*
Lecture Notes in Computer Science
*

We study different models

doi:10.1007/978-3-642-40988-2_33
fatcat:kopoglsadbhdtolo7ndnfcdvs4
*for*the random graphs and characterize the conditions when the planted*biclique*can be recovered. ... We consider the problem of*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. ... As many adversarial attacks exist that render*exact*solutions*exponential*, we focus on approximations. ...##
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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 and test a new polynomial-

*time*approximation that on average yields 2% more roles than the optimum. ... Acknowledgement We thank Mehul Shah

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

##
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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 graphs by introducing the (p, q)-

doi:10.1145/2783258.2783385
dblp:conf/kdd/MitzenmacherPPT15
fatcat:gmn7sydbezhx3etolrwjameehu
*biclique*densest subgraph problem ((p,q)-*Biclique*-DSP), and devise an*exact**algorithm*that can treat both clique ... We also use our methods to study how the k-clique densest subgraphs change as a function of*time*in*time*-evolving networks*for*various small values of k. ... to the*exact**algorithm*. ...##
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On the Phase Transition of Finding a Biclique in a larger Bipartite Graph
[article]

2016
*
arXiv
*
pre-print

This behaviour is remarkably similar

arXiv:1609.05876v1
fatcat:ivnkhqa76re5bmuzmdy4y3l5yy
*for*problems of a number of different sizes. ... A key step*for*a successful phase transition study is identifying a suitable order parameter, when none is known. ... 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 ...##
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Optimizing adiabatic quantum program compilation using a graph-theoretic framework

2018
*
Quantum Information Processing
*

Additionally, while

doi:10.1007/s11128-018-1863-4
fatcat:yczohpipyzczbdwq7ptiyfrbhy
*finding*a single embedding is difficult, no generalized method is known*for*tuning embeddings to use minimal hardware resources. ... To address these barriers, we introduce a graph-theoretic framework*for*developing structured embedding*algorithms*. ... Acknowledgements The authors would like to thank Steve Reinhardt and the anonymous two reviewers*for*feedback. ...##
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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*. ...*Finding*such a maximum is NP-hard [1, Problem GT24], both in bipartite and arbitrary graphs. A naïve*exponential**algorithm*could simply enumerate every possible solution to*find*a maximum. ...##
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Phase Transition in Matched Formulas and a Heuristic for Biclique Satisfiability
[article]

2018
*
arXiv
*
pre-print

In this paper we describe a heuristic

arXiv:1808.01774v1
fatcat:7fita6pky5cgpgegzzdzz2jgom
*algorithm**for*recognizing whether a formula is*biclique*satisfiable and we evaluate it by experiments on random formulas. ... We have performed experiments to*find*a phase transition of property "being matched" with respect to the ratio m/n where m is the number of clauses and n is the number of variables of the input formula ... If we consider*bicliques*in B k*for*a fixed k, then the number of valid*bicliques*|B k | is polynomial in the size of ϕ but it can be*exponential*in i (*for*B ∞ the number can be*exponential*in the size ...##
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Using Unsupervised Learning for Data-driven Procurement Demand Aggregation

2021
*
AAAI Conference on Artificial Intelligence
*

We propose an unsupervised learning methodology

dblp:conf/aaai/ShahamWKNOWS21
fatcat:dqwqrgm2gbd2xpb4kkczfwxhtu
*for*efficiently mining such*bicliques*using a novel Monte Carlo subspace clustering approach. ... The final performance was 71% of past cases transformed into bulk tenders correctly detected by the engine;*for*new opportunities pointed out by the engine 81% were deemed useful*for*potential bulk tender ... The computational complexity of*finding*the maximum*biclique*depends on the*exact*objective function used. ...
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