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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 ).  ...  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.  ... 
doi:10.1016/j.ipl.2010.10.020 fatcat:auug2gskdfelrpykz5mrvyswwm

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

An exact exponential time algorithm for counting bipartite cliques

Konstantin Kutzkov
2012 Information Processing Letters  
We achieve running 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.  ... 
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 perform a theoretical investigation of the concise representation problem and link it to the 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  ... 
doi:10.1145/1557019.1557069 dblp:conf/kdd/JinXL09 fatcat:bpt55h3qazbmjgwung5stkqskq

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.  ...  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 .  ... 
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.  ...  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 .  ... 
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] .  ...  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.  ... 
doi:10.3390/a10040113 fatcat:j6iugkrov5clfjnhjquh6y3zwm

Detecting Bicliques in GF[q] [chapter]

Jan Ramon, Pauli Miettinen, Jilles Vreeken
2013 Lecture Notes in Computer Science  
We study different models 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.  ... 
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 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.  ... 
doi:10.1145/1377836.1377838 dblp:conf/sacmat/EneHMRST08 fatcat:wxllge3kirbnlfwey4yynse7jy

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  ...  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.  ... 
doi:10.1145/2783258.2783385 dblp:conf/kdd/MitzenmacherPPT15 fatcat:gmn7sydbezhx3etolrwjameehu

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

Roberto Alonso, Raúl Monroy, Eduardo Aguirre
2016 arXiv   pre-print
This behaviour is remarkably similar 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  ... 
arXiv:1609.05876v1 fatcat:ivnkhqa76re5bmuzmdy4y3l5yy

Optimizing adiabatic quantum program compilation using a graph-theoretic framework

Timothy D. Goodrich, Blair D. Sullivan, Travis S. Humble
2018 Quantum Information Processing  
Additionally, while 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.  ... 
doi:10.1007/s11128-018-1863-4 fatcat:yczohpipyzczbdwq7ptiyfrbhy

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.  ...  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.  ... 
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.  ...  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  ... 
arXiv:1808.01774v1 fatcat:7fita6pky5cgpgegzzdzz2jgom

Using Unsupervised Learning for Data-driven Procurement Demand Aggregation

Eran Shaham, Adam Westerski, Rajaraman Kanagasabai, Amudha Narayanan, Samuel Ong, Jiayu Wong, Manjeet Singh
2021 AAAI Conference on Artificial Intelligence  
We propose an unsupervised learning methodology 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.  ... 
dblp:conf/aaai/ShahamWKNOWS21 fatcat:dqwqrgm2gbd2xpb4kkczfwxhtu
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