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Exact exponential-time algorithms for finding bicliques

Daniel Binkele-Raible, Henning Fernau, Serge Gaspers, Mathieu Liedloff
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.  ... 
doi:10.1016/j.ipl.2010.10.020 fatcat:auug2gskdfelrpykz5mrvyswwm

An exact exponential time algorithm for counting bipartite cliques

Konstantin Kutzkov
2012 Information Processing Letters  
We present 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.  ... 
doi:10.1016/j.ipl.2012.04.001 fatcat:yol6ix5pcrcubojgoxekfxkfja

Cartesian contour

Ruoming Jin, Yang Xiang, Lin Liu
2009 Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '09  
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.  ...  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.  ... 
doi:10.1145/1557019.1557069 dblp:conf/kdd/JinXL09 fatcat:bpt55h3qazbmjgwung5stkqskq

Obtaining Maximal Concatenated Phylogenetic Data Sets from Large Sequence Databases

M. J. Sanderson
2003 Molecular biology and evolution  
We developed an 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.  ... 
doi:10.1093/molbev/msg115 pmid:12777519 fatcat:j3bx2qsenbhzxnrdr3r4ef2jdy

On Independent Sets and Bicliques in Graphs [chapter]

Serge Gaspers, Dieter Kratsch, Mathieu Liedloff
2008 Lecture Notes in Computer Science  
Our major contribution is an 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 .  ... 
doi:10.1007/978-3-540-92248-3_16 fatcat:wlzqjssmzfadzmhhk3grlih6oa

On Independent Sets and Bicliques in Graphs

Serge Gaspers, Dieter Kratsch, Mathieu Liedloff
2010 Algorithmica  
Our major contribution is an 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 .  ... 
doi:10.1007/s00453-010-9474-1 fatcat:mfks63jsivgf3j5waurcs7klt4

Scale Reduction Techniques for Computing Maximum Induced Bicliques

Shahram Shahinpour, Shirin Shirvani, Zeynep Ertem, Sergiy Butenko
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.  ... 
doi:10.3390/a10040113 fatcat:j6iugkrov5clfjnhjquh6y3zwm

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

Michael Mitzenmacher, Jakub Pachocki, Richard Peng, Charalampos Tsourakakis, Shen Chen Xu
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)-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.  ... 
doi:10.1145/2783258.2783385 dblp:conf/kdd/MitzenmacherPPT15 fatcat:gmn7sydbezhx3etolrwjameehu

Detecting Bicliques in GF[q] [chapter]

Jan Ramon, Pauli Miettinen, Jilles Vreeken
2013 Lecture Notes in Computer Science  
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.  ...  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.  ... 
doi:10.1007/978-3-642-40988-2_33 fatcat:kopoglsadbhdtolo7ndnfcdvs4

Fast exact and heuristic methods for role minimization problems

Alina Ene, William Horne, Nikola Milosavljevic, Prasad Rao, Robert Schreiber, Robert E. Tarjan
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.  ... 
doi:10.1145/1377836.1377838 dblp:conf/sacmat/EneHMRST08 fatcat:wxllge3kirbnlfwey4yynse7jy

Optimizing adiabatic quantum program compilation using a graph-theoretic framework

Timothy D. Goodrich, Blair D. Sullivan, Travis S. Humble
2018 Quantum Information Processing  
To address these barriers, we introduce 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.  ... 
doi:10.1007/s11128-018-1863-4 fatcat:yczohpipyzczbdwq7ptiyfrbhy

On the Phase Transition of Finding a Biclique in a larger Bipartite Graph [article]

Roberto Alonso, Raúl Monroy, Eduardo Aguirre
2016 arXiv   pre-print
We report on the phase transition of 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  ... 
arXiv:1609.05876v1 fatcat:ivnkhqa76re5bmuzmdy4y3l5yy

An Exact Branch and Bound Algorithm with Symmetry Breaking for the Maximum Balanced Induced Biclique Problem [chapter]

Ciaran McCreesh, Patrick Prosser
2014 Lecture Notes in Computer Science  
We show how techniques from state-of-the-art branch and bound 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.  ... 
doi:10.1007/978-3-319-07046-9_16 fatcat:ospxjhttr5gxtkgw7oy3iyhddi

Phase Transition in Matched Formulas and a Heuristic for Biclique Satisfiability [article]

Miloš Chromý Charles University, Faculty of Mathematics and Physics, Department of Theoretical Computer Science, Mathematical Logic)
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.  ... 
arXiv:1808.01774v1 fatcat:7fita6pky5cgpgegzzdzz2jgom

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

Timothy D. Goodrich and Travis S. Humble and Blair D. Sullivan
2017 arXiv   pre-print
To address these barriers, we introduce 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.  ... 
arXiv:1704.01996v2 fatcat:55xateudzff4lpudukl5rdxjq4
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