Article

Learning and Verifying Graphs Using Queries with a Focus on Edge Counting

Authors:

Lev Reyzin,

Nikhil SrivastavaAuthors Info & Claims

ALT '07: Proceedings of the 18th international conference on Algorithmic Learning Theory

Pages 285 - 297

https://doi.org/10.1007/978-3-540-75225-7_24

Published: 01 October 2007 Publication History

Abstract

We consider the problem of learning and verifying hidden graphs and their properties given query access to the graphs. We analyze various queries (edge detection, edge counting, shortest path), but we focus mainly on edge counting queries. We give an algorithm for learning graph partitions using O ( n log n ) edge counting queries. We introduce a problem that has not been considered: verifying graphs with edge counting queries, and give a randomized algorithm with error ï for graph verification using O (log(1/ ï )) edge counting queries. We examine the current state of the art and add some original results for edge detection and shortest path queries to give a more complete picture of the relative power of these queries to learn various graph classes. Finally, we relate our work to Freivalds' `fingerprinting technique' --- a probabilistic method for verifying that two matrices are equal by multiplying them by random vectors.

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Cited By

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Rong GYang YLi WWang J(2022)A divide-and-conquer approach for reconstruction of {C ≥5}-free graphs via betweenness queriesTheoretical Computer Science10.1016/j.tcs.2022.03.008917:C(1-11)Online publication date: 25-May-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.03.008
Beame PHar-Peled SRamamoorthy SRashtchian CSinha M(2020)Edge Estimation with Independent Set OraclesACM Transactions on Algorithms10.1145/340486716:4(1-27)Online publication date: 16-Sep-2020
https://dl.acm.org/doi/10.1145/3404867
Wang ZHonorio J(2019)Reconstructing a Bounded-Degree Directed Tree Using Path Queries2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)10.1109/ALLERTON.2019.8919924(506-513)Online publication date: 24-Sep-2019
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Index Terms

Learning and Verifying Graphs Using Queries with a Focus on Edge Counting
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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Published In

ALT '07: Proceedings of the 18th international conference on Algorithmic Learning Theory

October 2007

402 pages

ISBN:9783540752240

Editors:
Marcus Hutter
RSISE @ ANU and SML @ NICTA, Canberra,, Australia ACT, 0200
,
Rocco A. Servedio
Columbia University, New York, USA NY, P.O. Box
,
Eiji Takimoto
Graduate School of Information Sciences, Tohoku University,, Japan Sendai 980-8579

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 October 2007

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Rong GYang YLi WWang J(2022)A divide-and-conquer approach for reconstruction of {C ≥5}-free graphs via betweenness queriesTheoretical Computer Science10.1016/j.tcs.2022.03.008917:C(1-11)Online publication date: 25-May-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.03.008
Beame PHar-Peled SRamamoorthy SRashtchian CSinha M(2020)Edge Estimation with Independent Set OraclesACM Transactions on Algorithms10.1145/340486716:4(1-27)Online publication date: 16-Sep-2020
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