Finding hidden hubs and dominating sets in sparse graphs by randomized neighborhood queries

Damaschke, Peter

doi:10.1002/net.20404

Cited by 2 publications

(1 citation statement)

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“…Since the degrees d of vertices in interaction networks are very different and tests are time-consuming, we arrive again at the type of problem discussed above. In [13] we studied a similar problem with more powerful, nonbinary queries that return all interaction partners of a bait.…”

Section: Introductionmentioning

confidence: 99%

Competitive Group Testing and Learning Hidden Vertex Covers With Minimum Adaptivity

Damaschke

Muhammad

2010

Discrete Math. Algorithm. Appl.

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Suppose that we are given a set of n elements d of which have a property called defective. A group test can check for any subset, called a pool, whether it contains a defective. It is known that a nearly optimal number of O(d log(n/d)) pools in two stages (where tests within a stage are done in parallel) are sufficient, but then the searcher must know d in advance. Here we explore group testing strategies that use a nearly optimal number of pools and a few stages although d is not known beforehand. We prove a lower bound of Ω(log d/ log log d) stages and more general pools versus stages tradeoff. This is almost tight, since O(log d) stages are sufficient for a strategy with O(d log n) pools. As opposed to this negative result, we devise a randomized strategy using O(d log(n/d)) pools in three stages, with any desired success probability 1 − . With some additional measures even two stages are enough. Open questions concern the optimal constant factors and practical implications. A related problem motivated by biological network analysis is to learn hidden vertex covers of a small size k in unknown graphs by edge group tests. (Does a given subset of vertices contain an edge?) We give a one-stage strategy using O(k 3 log n) pools, with any parameterized algorithm for vertex cover enumeration as a decoder. During the course of this work we also provide a classification of types of randomized search strategies in general. 84-95. 291 Discrete Math. Algorithm. Appl. 2010.02:291-311. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 03/11/15. For personal use only. 292 P. Damaschke & A. S. Muhammad choose arbitrary subsets Q ⊂ X called pools, and ask whether Q contains at least one defective. Nondefective elements are called negative. A positive pool is a pool containing some defective, thus responding Yes to a group test. A negative pool is a pool without defectives, thus responding No to a group test.Group testing has several applications, most notably in biological and chemical testing, but also in communication networks, information gathering, compression, streaming algorithms, etc., see for instance [9,10,15,[20][21][22] and further pointers therein.Throughout this paper, log means log 2 if no other base is mentioned. By the information-theoretic lower bound, at least log n d ≈ d log(n/d) pools are needed to find d defectives even if the number d is known in advance, and it is an easy exercise to devise an adaptive query strategy using O(d log(n/d)) pools. Here, a strategy is called adaptive if queries are asked sequentially, that is, every pool can be prepared based on the outcomes of all earlier queries. For many applications however, the time consumption of adaptive strategies is hardly acceptable, and strategies that work in a few stages are strongly preferred: The pools for every stage must be prepared in advance, depending on the outcomes of earlier stages, and then they are queried in parallel.Any one-stage strategy needs Ω(d 2 log n/ log d) pools, as a consequence of ...

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Section: Introductionmentioning

confidence: 99%

Competitive Group Testing and Learning Hidden Vertex Covers With Minimum Adaptivity

Damaschke

Muhammad

2010

Discrete Math. Algorithm. Appl.

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Node sampling for protein complex estimation in bait-prey graphs

Scholtens

Spencer

2015

Statistical Applications in Genetics and Molecular Biology

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In cellular biology, node-and-edge graph or "network" data collection often uses bait-prey technologies such as co-immunoprecipitation (CoIP). Bait-prey technologies assay relationships or "interactions" between protein pairs, with CoIP specifically measuring protein complex co-membership. Analyses of CoIP data frequently focus on estimating protein complex membership. Due to budgetary and other constraints, exhaustive assay of the entire network using CoIP is not always possible. We describe a stratified sampling scheme to select baits for CoIP experiments when protein complex estimation is the main goal. Expanding upon the classic framework in which nodes represent proteins and edges represent pairwise interactions, we define generalized nodes as sets of adjacent nodes with identical adjacency outside the set and use these as strata from which to select the next set of baits. Strata are redefined at each round of sampling to incorporate accumulating data. This scheme maintains user-specified quality thresholds for protein complex estimates and, relative to simple random sampling, leads to a marked increase in the number of correctly estimated complexes at each round of sampling. The R package seqSample contains all source code and is available at http://vault.northwestern.edu/~dms877/Rpacks/.

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Finding hidden hubs and dominating sets in sparse graphs by randomized neighborhood queries

Cited by 2 publications

References 17 publications

Competitive Group Testing and Learning Hidden Vertex Covers With Minimum Adaptivity

Competitive Group Testing and Learning Hidden Vertex Covers With Minimum Adaptivity

Node sampling for protein complex estimation in bait-prey graphs

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