Non-adaptive learning of a hidden hypergraph

Abstract We give a new deterministic algorithm that non-adaptively learns a hidden hypergraph from edge-detecting queries. All previous non-adaptive algorithms either run in exponential time or have non-optimal query complexity. We give the first polynomial time non-adaptive learning algorithm for learning hypergraphs that asks an almost optimal number of queries.

[1]  Siu-Ming Yiu,et al.  Non-adaptive Complex Group Testing with Multiple Positive Sets , 2011, TAMC.

[2]  Nader H. Bshouty,et al.  Linear Time Constructions of Some d -Restriction Problems , 2014, CIAC.

[3]  Noga Alon,et al.  Learning a Hidden Subgraph , 2005, SIAM J. Discret. Math..

[4]  Frank K. Hwang,et al.  A survey on nonadaptive group testing algorithms through the angle of decoding , 2008, J. Comb. Optim..

[5]  Lie Zhu,et al.  Some New Bounds for Cover-Free Families , 2000, J. Comb. Theory, Ser. A.

[6]  Ruizhong Wei,et al.  On a Bound of Cover-Free Families , 2004, Des. Codes Cryptogr..

[7]  Mathilde Bouvel,et al.  Combinatorial Search on Graphs Motivated by Bioinformatics Applications: A Brief Survey , 2005, WG.

[8]  David C. Torney,et al.  Sets pooling designs , 1999 .

[9]  Sergey Yekhanin,et al.  Trivial two-stage group testing for complexes using almost disjunct matrices , 2004, Discret. Appl. Math..

[10]  Hung-Lin Fu,et al.  Learning a hidden graph , 2014, Optim. Lett..

[11]  Nader H. Bshouty,et al.  Testers and their applications , 2014, ITCS.

[12]  Hung-Lin Fu,et al.  Reconstruction of hidden graphs and threshold group testing , 2011, J. Comb. Optim..

[13]  Anthony J. Macula,et al.  A group testing method for finding patterns in data , 2004, Discret. Appl. Math..

[14]  Nader H. Bshouty,et al.  Exact Learning from Membership Queries: Some Techniques, Results and New Directions , 2013, ALT.

[15]  Arkadii G. D'yachkov,et al.  Families of Finite Sets in which No Intersection of Sets Is Covered by the Union of s Others , 2002, J. Comb. Theory A.

[16]  D. Angluin Queries and Concept Learning , 1988 .

[17]  Dana Angluin,et al.  Learning a Hidden Hypergraph , 2005, J. Mach. Learn. Res..

[18]  Nikhil Srivastava,et al.  Learning and Verifying Graphs Using Queries with a Focus on Edge Counting , 2007, ALT.

[19]  Lisa Hellerstein,et al.  Attribute-efficient learning in query and mistake-bound models , 1996, COLT '96.

[20]  Weili Wu,et al.  Construction of d(H)-disjunct matrix for group testing in hypergraphs , 2006, J. Comb. Optim..

[21]  Noga Alon,et al.  Learning a Hidden Matching , 2004, SIAM J. Comput..

[22]  D. Du,et al.  Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing , 2006 .

[23]  Douglas R Stinson,et al.  New constructions for perfect hash families and related structures using combinatorial designs and codes , 2000 .

[24]  Nader H. Bshouty,et al.  Asking questions to minimize errors , 1993, COLT '93.

[25]  Richard C. Singleton,et al.  Nonrandom binary superimposed codes , 1964, IEEE Trans. Inf. Theory.

[26]  Fedor V. Fomin,et al.  Efficient Computation of Representative Sets with Applications in Parameterized and Exact Algorithms , 2013, SODA.

[27]  Noga Alon,et al.  Algorithmic construction of sets for k-restrictions , 2006, TALG.

[28]  Dana Angluin,et al.  Learning a hidden graph using O(logn) queries per edge , 2008, J. Comput. Syst. Sci..

[29]  Vladimir Grebinski,et al.  Reconstructing a Hamiltonian Cycle by Querying the Graph: Application to DNA Physical Mapping , 1998, Discret. Appl. Math..

[30]  Nader H. Bshouty,et al.  On Exact Learning Monotone DNF from Membership Queries , 2014, ALT.

[31]  Nader H. Bshouty,et al.  Almost Optimal Cover-Free Families , 2015, CIAC.

[32]  Noga Alon,et al.  An optimal procedure for gap closing in whole genome shotgun sequencing , 2001, RECOMB.