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Graph Reconstruction and Verification

Authors:

Sampath Kannan,

Claire Mathieu,

Hang ZhouAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 14, Issue 4

Article No.: 40, Pages 1 - 30

https://doi.org/10.1145/3199606

Published: 09 August 2018 Publication History

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Abstract

How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? We assume that the unknown graph G is connected, unweighted, and has bounded degree. In the reconstruction problem, the goal is to find the graph G. In the verification problem, we are given a hypothetical graph Ĝ and want to check whether G is equal to Ĝ.

We provide a randomized algorithm for reconstruction using Õ(n^3/2) distance queries, based on Voronoi cell decomposition. Next, we analyze natural greedy algorithms for reconstruction using a shortest path oracle and also for verification using either oracle, and show that their query complexity is n^1+o(1). We further improve the query complexity when the graph is chordal or outerplanar. Finally, we show some lower bounds, and consider an approximate version of the reconstruction problem.

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https://doi.org/10.1109/TPDS.2022.3205219
Duoyi ZJiafeng ZZiyue M(2023)Reconfiguration Scheme Design of DRDES based on Simulated Annealing Algorithm2023 China Automation Congress (CAC)10.1109/CAC59555.2023.10450736(1079-1084)Online publication date: 17-Nov-2023
https://doi.org/10.1109/CAC59555.2023.10450736
Bastide PCook LErickson JGroenland CKreveld MMannens IVermeulen J(2023)Reconstructing Graphs from Connected TriplesGraph-Theoretic Concepts in Computer Science10.1007/978-3-031-43380-1_2(16-29)Online publication date: 28-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43380-1_2
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Index Terms

Graph Reconstruction and Verification
1. Networks
  1. Network algorithms
2. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
    2. Graph algorithms analysis

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 14, Issue 4

October 2018

445 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3266298

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 August 2018

Accepted: 01 March 2018

Revised: 01 October 2017

Received: 01 February 2017

Published in TALG Volume 14, Issue 4

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French Agence Nationale de la Recherche
Lise Meitner Award Fellowship
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Cited By

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https://doi.org/10.1109/TPDS.2022.3205219
Duoyi ZJiafeng ZZiyue M(2023)Reconfiguration Scheme Design of DRDES based on Simulated Annealing Algorithm2023 China Automation Congress (CAC)10.1109/CAC59555.2023.10450736(1079-1084)Online publication date: 17-Nov-2023
https://doi.org/10.1109/CAC59555.2023.10450736
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https://dl.acm.org/doi/10.1007/978-3-031-43380-1_2
Mathieu CZhou H(2023)A simple algorithm for graph reconstructionRandom Structures & Algorithms10.1002/rsa.2114363:2(512-532)Online publication date: 16-Feb-2023
https://doi.org/10.1002/rsa.21143
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
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Wei QHu G(2021)Unifying Node Labels, Features, and Distances for Deep Network CompletionEntropy10.3390/e2306077123:6(771)Online publication date: 18-Jun-2021
https://doi.org/10.3390/e23060771
Afshar RGoodrich MMatias POsegueda MAgrawal KAzar Y(2021)Parallel Network Mapping AlgorithmsProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461822(410-413)Online publication date: 6-Jul-2021
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Rong GLi WYang YWang J(2021)Reconstruction and verification of chordal graphs with a distance oracleTheoretical Computer Science10.1016/j.tcs.2021.01.006859(48-56)Online publication date: Mar-2021
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Erlebach T(2021)Algorithms that Access the Input via QueriesSOFSEM 2021: Theory and Practice of Computer Science10.1007/978-3-030-67731-2_1(3-12)Online publication date: 25-Jan-2021
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Bonnet ÉCabello SMohar BPérez-Rosés H(2020)The Inverse Voronoi Problem in Graphs I: HardnessAlgorithmica10.1007/s00453-020-00716-482:10(3018-3040)Online publication date: 1-Oct-2020
https://dl.acm.org/doi/10.1007/s00453-020-00716-4

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