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research-article

Topology recognition with advice

Authors:

Emanuele G. Fusco,

Rossella PetreschiAuthors Info & Claims

Information and Computation, Volume 247, Issue C

Pages 254 - 265

https://doi.org/10.1016/j.ic.2016.01.005

Published: 01 April 2016 Publication History

Abstract

In topology recognition, each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such information can be provided to nodes as advice. An oracle knowing the network can give a (possibly different) string of bits to each node, and all nodes must reconstruct the network using this advice, after a given number of rounds of communication. During each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. The time of completing topology recognition is the number of rounds it takes, and the size of advice is the maximum length of a string given to nodes.We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size n and diameter D α n, for any constant α < 1 . In most cases, our bounds are asymptotically tight.

References

[1]

S. Abiteboul, H. Kaplan, T. Milo, Compact labeling schemes for ancestor queries, in: Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms, 2001, pp. 547-556.

[2]

D. Angluin, Local and global properties in networks of processors, in: Proc. 12th Annual ACM Symposium on Theory of Computing, 1980, pp. 82-93.

[3]

H. Attiya, M. Snir, M. Warmuth, Computing on an anonymous ring, J. ACM, 35 (1988) 845-875.

Digital Library

[4]

H. Attiya, A. Bar-Noy, D. Dolev, D. Koller, D. Peleg, R. Reischuk, Renaming in an asynchronous environment, J. ACM, 37 (1990) 524-548.

Digital Library

[5]

B. Awerbuch, Optimal distributed algorithms for minimum weight spanning tree, counting, leader election and related problems, in: Proc. 19th Annual ACM Symposium on Theory of Computing, 1987, pp. 230-240.

Digital Library

[6]

P. Boldi, S. Vigna, Computing anonymously with arbitrary knowledge, in: Proc. 18th ACM Symposium on Principles of Distributed Computing, 1999, pp. 181-188.

[7]

S. Caminiti, I. Finocchi, R. Petreschi, Engineering tree labeling schemes: a case study on least common ancestor, in: Proc. 16th Annual European Symposium on Algorithms, 2008, pp. 234-245.

[8]

J. Chalopin, S. Das, A. Kosowski, Constructing a map of an anonymous graph: applications of universal sequences, in: Proc. 14th International Conference on Principles of Distributed Systems, 2010, pp. 119-134.

[9]

R. Cohen, P. Fraigniaud, D. Ilcinkas, A. Korman, D. Peleg, Label-guided graph exploration by a finite automaton, ACM Trans. Algorithms, 4 (2008).

[10]

D. Dereniowski, A. Pelc, Drawing maps with advice, J. Parallel Distrib. Comput., 72 (2012) 132-143.

Digital Library

[11]

Y. Emek, P. Fraigniaud, A. Korman, A. Rosen, Online computation with advice, Theor. Comput. Sci., 412 (2011) 2642-2656.

Digital Library

[12]

Y. Emek, C. Pfister, J. Seidel, R. Wattenhofer, Anonymous networks: randomization = 2-hop coloring, in: Proc. 32nd ACM Symposium on Principles of Distributed Computing, 2014, pp. 96-105.

[13]

Y. Emek, J. Seidel, R. Wattenhofer, Computability in anonymous networks: revocable vs. irrecovable outputs, in: Proc. 41th International Colloquium on Automata, Languages and Programming, 2014, pp. 183-195.

[14]

P. Fraigniaud, C. Gavoille, D. Ilcinkas, A. Pelc, Distributed computing with advice: information sensitivity of graph coloring, Distrib. Comput., 21 (2009) 395-403.

Digital Library

[15]

P. Fraigniaud, D. Ilcinkas, A. Pelc, Communication algorithms with advice, J. Comput. Syst. Sci., 76 (2010) 222-232.

Digital Library

[16]

P. Fraigniaud, D. Ilcinkas, A. Pelc, Tree exploration with advice, Inf. Comput., 206 (2008) 1276-1287.

Digital Library

[17]

P. Fraigniaud, A. Korman, E. Lebhar, Local MST computation with short advice, Theory Comput. Syst., 47 (2010) 920-933.

Digital Library

[18]

E. Fusco, A. Pelc, Trade-offs between the size of advice and broadcasting time in trees, Algorithmica, 60 (2011) 719-734.

Digital Library

[19]

E. Fusco, A. Pelc, How much memory is needed for leader election, Distrib. Comput., 24 (2011) 65-78.

Digital Library

[20]

C. Gavoille, D. Peleg, S. Pérennes, R. Raz, Distance labeling in graphs, J. Algorithms, 53 (2004) 85-112.

Digital Library

[21]

D.S. Hirschberg, J.B. Sinclair, Decentralized extrema-finding in circular configurations of processes, Commun. ACM, 23 (1980) 627-628.

Digital Library

[22]

D. Ilcinkas, D. Kowalski, A. Pelc, Fast radio broadcasting with advice, Theor. Comput. Sci., 411 (2012) 1544-1557.

Digital Library

[23]

M. Katz, N. Katz, A. Korman, D. Peleg, Labeling schemes for flow and connectivity, SIAM J. Comput., 34 (2004) 23-40.

Digital Library

[24]

A. Korman, S. Kutten, D. Peleg, Proof labeling schemes, Distrib. Comput., 22 (2010) 215-233.

Digital Library

[25]

E. Kranakis, D. Krizanc, J. van der Berg, Computing Boolean functions on anonymous networks, Inf. Comput., 114 (1994) 214-236.

Digital Library

[26]

N. Nisse, D. Soguet, Graph searching with advice, Theor. Comput. Sci., 410 (2009) 1307-1318.

Digital Library

[27]

D. Peleg, Distributed computing, a locality-sensitive approach, SIAM, Philadelphia, 2000.

Digital Library

[28]

G.L. Peterson, An O ( n log ¿ n ) unidirectional distributed algorithm for the circular extrema problem, ACM Trans. Program. Lang. Syst., 4 (1982) 758-762.

Digital Library

[29]

S. Tani, Compression of view on anonymous networks-Folded view-, IEEE Trans. Parallel Distrib. Syst., 23 (2012) 255-262.

Digital Library

[30]

M. Thorup, U. Zwick, Approximate distance oracles, J. ACM, 52 (2005) 1-24.

Digital Library

[31]

M. Yamashita, T. Kameda, Computing on anonymous networks: part I-characterizing the solvable cases, IEEE Trans. Parallel Distrib. Syst., 7 (1996) 69-89.

Digital Library

Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Gańczorz AJurdziński TLewko MPelc A(2023)Deterministic size discovery and topology recognition in radio networks with short labelsInformation and Computation10.1016/j.ic.2023.105010292:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.ic.2023.105010
Dhar AGorain BMondal KPatra SSingh R(2023)Edge exploration of anonymous graph by mobile agent with external helpComputing10.1007/s00607-022-01136-8105:2(483-506)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1007/s00607-022-01136-8
Show More Cited By

Topology recognition with advice
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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cover image Information and Computation

Information and Computation Volume 247, Issue C

April 2016

314 pages

ISSN:0890-5401

Issue’s Table of Contents

Copyright © Elsevier Inc.

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 April 2016

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Cited By

Balliu ABrandt SKuhn FNowicki KOlivetti DRotenberg ESuomela JKuznetsov PGelles ROlivetti D(2024)Brief Announcement: Local Advice and Local DecompressionProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662805(117-120)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662805
Gańczorz AJurdziński TLewko MPelc A(2023)Deterministic size discovery and topology recognition in radio networks with short labelsInformation and Computation10.1016/j.ic.2023.105010292:COnline publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1016/j.ic.2023.105010
Dhar AGorain BMondal KPatra SSingh R(2023)Edge exploration of anonymous graph by mobile agent with external helpComputing10.1007/s00607-022-01136-8105:2(483-506)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1007/s00607-022-01136-8
Gorain B Miller APelc A(2023)Four shades of deterministic leader election in anonymous networksDistributed Computing10.1007/s00446-023-00451-336:4(419-449)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s00446-023-00451-3
Gańczorz AJurdziński TLewko MPelc AAgrawal KAzar Y(2021)Deterministic Size Discovery and Topology Recognition in Radio Networks with Short LabelsProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461821(432-434)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461821
Gorain BMiller APelc AAgrawal KAzar Y(2021)Four Shades of Deterministic Leader Election in Anonymous NetworksProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461794(265-274)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461794
Ellen FGorain BMiller APelc AScheideler CBerenbrink P(2019)Constant-Length Labeling Schemes for Deterministic Radio BroadcastThe 31st ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3323165.3323194(171-178)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3323165.3323194
Dieudonné YPelc A(2019)Impact of Knowledge on Election Time in Anonymous NetworksAlgorithmica10.1007/s00453-018-0444-381:1(238-288)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1007/s00453-018-0444-3
Gorain BPelc A(2018)Deterministic Graph Exploration with AdviceACM Transactions on Algorithms10.1145/328082315:1(1-17)Online publication date: 16-Nov-2018
https://dl.acm.org/doi/10.1145/3280823
Gorain BPelc A(2018)Finding the Size of a Radio Network with Short LabelsProceedings of the 19th International Conference on Distributed Computing and Networking10.1145/3154273.3154298(1-10)Online publication date: 4-Jan-2018
https://dl.acm.org/doi/10.1145/3154273.3154298
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