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Broutin, Nicolas; Devroye, Luc; McLeish, Erin

doi:10.1002/rsa.v32:4

Cited by 18 publications

(3 citation statements)

References 122 publications

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“…Moreover, he showed that any algorithm achieving better than a 2-approximation must use a nearly linear number of degree queries. Goldreich and Ron [GR08] showed that by using both degree and neighbor queries, the approximation improves to (1 − ε)m ≤ m ≤ (1 + ε)m by using √ n poly(log n, 1/ε) queries. It is worth nothing that Feige [Fei06] and Goldreich and Ron [GR08] have identified certain hard instances showing that these upper bounds cannot be improved, up to polylog factors.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…We provide an auxiliary degree estimation result, connecting BIS queries to local queries (e.g., [Fei06,GR08]).…”

Section: Degree Estimation Using Bis Queriesmentioning

confidence: 99%

“…Previous work on graph parameter estimation has primarily focused on local queries, such as (i) degree queries (which output the degree of a vertex v), (ii) edge existence queries (which answer whether a pair {u, v} forms an edge), or (iii) neighbor queries (which provide the i th neighbor of a vertex v). However, such queries cannot achieve sub-polynomial query costs on certain graphs identified by Feige [Fei06] and Goldreich and Ron [GR08]. These queries can only obtain local information about the graph.…”

Section: Introductionmentioning

confidence: 99%

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Edge Estimation with Independent Set Oracles

Beame¹,

Har-Peled²,

Ramamoorthy³

et al. 2017

Preprint

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We study the task of estimating the number of edges in a graph with access to only an independent set oracle. Independent set queries draw motivation from group testing and have applications to the complexity of decision versus counting problems. We give two algorithms to estimate the number of edges in an n-vertex graph, using (i) polylog(n) bipartite independent set queries, or (ii) n 2/3 polylog(n) independent set queries.

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Section: Motivation and Related Workmentioning

confidence: 99%

“…We provide an auxiliary degree estimation result, connecting BIS queries to local queries (e.g., [Fei06,GR08]).…”

Section: Degree Estimation Using Bis Queriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Edge Estimation with Independent Set Oracles

Beame¹,

Har-Peled²,

Ramamoorthy³

et al. 2017

Preprint

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On ultrametric 1-median selection

Chang

2020

Theoretical Computer Science

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Introduction to Random Graphs

2015

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From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

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Untitled

Cited by 18 publications

References 122 publications

Edge Estimation with Independent Set Oracles

Edge Estimation with Independent Set Oracles

On ultrametric 1-median selection

Introduction to Random Graphs

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