research-article

Modelling gateway placement in wireless networks: geometric k-centres of unit disc graphs

Authors:

Stephane Durocher,

Krishnam Raju Jampani,

Lata NarayananAuthors Info & Claims

DIALM-POMC '08: Proceedings of the fifth international workshop on Foundations of mobile computing

Pages 79 - 86

https://doi.org/10.1145/1400863.1400879

Published: 18 August 2008 Publication History

Abstract

Motivated by the gateway placement problem in wireless networks, we consider the geometric k-centre problem on unit disc graphs: given a set of points P in the plane, find a set F of k points in the plane that minimizes the maximum graph distance from any vertex in P to the nearest vertex in F in the unit disc graph induced by P union F. We describe exact and approximate polynomial-time solutions to this problem for any fixed k and show that the problem is NP-hard when k is an arbitrary input parameter.

References

[1]

B. Aoun, R. Boutaba, and Y. Iraqi. Gateway placement optimization in WMN with QoS constraints. IEEE Journal on Selected Areas in Communications (JSAC), 11:2127--2136, 2006.

Digital Library

[2]

P. Bose. Visibility in simple polygons. Master's thesis, University of Waterloo, 1991.

[3]

P. Bose, A. Lubiw, and J. I. Munro. Efficient visibility queries in simple polygons. Computational Geometry: Theory and Applications, 23(3):313--335, 2002.

Digital Library

[4]

P. Bose, P. Morin, I. Stojmenovic, and J. Urrutia. Routing with guaranteed delivery in ad hoc wireless networks. Wireless Networks, 7:609--616, 2001.

Digital Library

[5]

H. Breu. Algorithmic Aspects of Constrained Unit Disk Graphs. PhD thesis, University of British Columbia, 1996.

Digital Library

[6]

H. Breu and D. Kirkpatrick. Unit disk graph recognition is NP-hard. Computational Geometry: Theory and Applications, 9(1--2):3--24, 1998.

Digital Library

[7]

T. M. Chan. All-pairs shortest paths for unweighted undirected graphs in o(mn) time. In Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 514--523, 2006.

Digital Library

[8]

B. M. Chazelle and D. T. Lee. On a circle placement problem. Computing, 36(1--2):1--16, 1986.

Digital Library

[9]

B. Clark, C. Colbourn, and D. Johnson. Unit disk graphs. Discrete Mathematics, 86(1--3):165--177, 1991.

Digital Library

[10]

A. Efrat, S. P. Fekete, P. R. Gaddehosur, J. S. B. Mitchell, V. Polishchuk, and J. Suomela. Improved approximation algorithms for relay placement. In Proceedings of the European Symposium on Algorithms (ESA), Lecture Notes in Computer Science. Springer-Verlag, 2008. To appear.

Digital Library

[11]

W. K. Hale. Frequency assignment: Theory and applications. Proceedings of the IEEE, 68(12):1497--1514, 1980.

[12]

M. L. Huson and A. Sen. Broadcast scheduling algorithms for radio networks. In Proceedings of the IEEE Military Communications Conference, volume 2, pages 647--651, 1995.

[13]

O. Kariv and S. L. Hakimi. An algorithmic approach to network location problems I: The p-centers. SIAM Journal of Applied Mathematics, 37(3):513--538, 1979.

[14]

J. D. E. Konhauser, D. Velleman, and S. Wagon. Which Way Did the Bicycle Go? Mathematical Association of America, 1996.

[15]

F. Kuhn, T. Moscibroda, and R. Wattenhofer. Unit disk graph approximation. In ACM Joint Workshop on Foundations of Mobile Computing, 2004.

Digital Library

[16]

X.-Y. Li. Applications of computational geometry in wireless ad hoc networks. In X. Cheng, X. Huang, and D.-Z. Du, editors, Ad Hoc Wireless Networking. Kluwer, 2003.

[17]

X.-Y. Li and Y. Wang. Wireless sensor networks and computational geometry. In M. Ilyas et al., editor, Handbook of Sensor Networks. CRC Press, 2003.

[18]

M. V. Marathe, H. Breu, H. B. Hunt III, S. S. Ravi, and D. J. Rosenkrantz. Simple heuristics for unit disk graphs. Networks, 25(2):59--68, 1995.

[19]

S. Masuyama, T. Ibaraki, and T. Hasegawa. The computational complexity of the m-center problems in the plane. Transactions of IEICE, E64:57--64, 1981.

[20]

S. Mihandoust and L. Narayanan. Multiple sink positioning in sensor networks. In Proceedings of the International Workshop on Foundations of Mobile Computing (DIALM-POMC), 2007.

[21]

A. Tamir. Improved complexity bounds for center location problems on networks by using dynamic data structures. SIAM Journal on Discrete Mathematics, 1(3):377--396, 1988.

Digital Library

[22]

C. Toth, 2007. Personal communication.

Cited By

Yedidsion HAshur SBanik ACarmi PKatz MSegal M(2020)Sensor Network Topology Design and Analysis for Efficient Data Gathering by a Mobile MuleAlgorithmica10.1007/s00453-020-00704-8Online publication date: 22-Apr-2020
https://doi.org/10.1007/s00453-020-00704-8
Li YHuang SFan RZhang ZZhou Y(2017)Research on gateway deployment of WMN based on maximum coupling subgraph and PSO algorithmSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-015-1822-221:4(923-933)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1007/s00500-015-1822-2

Index Terms

Modelling gateway placement in wireless networks: geometric k-centres of unit disc graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

DIALM-POMC '08: Proceedings of the fifth international workshop on Foundations of mobile computing

August 2008

100 pages

ISBN:9781605582443

DOI:10.1145/1400863

General Chairs:
Michael Segal
Ben-Gurion of the Negev, Israel
,
Alexander Kesselman
Google Inc., USA

Copyright © 2008 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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Publication History

Published: 18 August 2008

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PODC '08

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PODC '08: ACM Symposium on Principles of Distributed Computing

August 18 - 21, 2008

Toronto, Canada

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DIALM-POMC '08 Paper Acceptance Rate 10 of 35 submissions, 29%;

Overall Acceptance Rate 21 of 68 submissions, 31%

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Cited By

Yedidsion HAshur SBanik ACarmi PKatz MSegal M(2020)Sensor Network Topology Design and Analysis for Efficient Data Gathering by a Mobile MuleAlgorithmica10.1007/s00453-020-00704-8Online publication date: 22-Apr-2020
https://doi.org/10.1007/s00453-020-00704-8
Li YHuang SFan RZhang ZZhou Y(2017)Research on gateway deployment of WMN based on maximum coupling subgraph and PSO algorithmSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-015-1822-221:4(923-933)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1007/s00500-015-1822-2

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