skip to main content
10.1145/1137856.1137901acmconferencesArticle/Chapter ViewAbstractPublication PagessocgConference Proceedingsconference-collections
Article

Minimum-cost load-balancing partitions

Published: 05 June 2006 Publication History

Abstract

We consider the problem of balancing the load among several service-providing facilities, while keeping the total cost low. Let D be the underlying demand region, and let p1, …, pm be m points representing m facilities. We consider the following problem: Subdivide D into m equal-area regions R1, …, Rm, so that region Ri is served by facility pi, and the average distance between a point q in D and the facility that serves q is minimal.We present constant-factor approximation algorithms for this problem, with the additional requirement that the resulting regions must be convex. As an intermediate result we show how to partition a convex polygon into m=2k equal-area convex subregions so that the fatness of the resulting regions is within a constant factor of the fatness of the original polygon. We also prove that our partition is, up to a constant factor, the best one can get if one's goal is to maximize the fatness of the least fat subregion.We also discuss the structure of the optimal partition for the aforementioned load balancing problem: indeed, we argue that it is always induced by an additive-weighted Voronoi diagram for an appropriate choice of weights.

References

[1]
P.K. Agarwal, A. Efrat, and M. Sharir. Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications. SIAM Journal on Computing, 29(3) (1999), 912--953.
[2]
P.K. Agarwal and M. Sharir. Efficient algorithms for geometric optimization. ACM Computing Surveys, 30(4) (1998), 412--458.
[3]
F. Aurenhammer, F. Hoffmann, and B. Aronov. Minkowski-type theorems and least-squares clustering. Algorithmica, 20(1) (1998), 61--76.
[4]
M. de Berg, M.J. Katz, A.F. van der Stappen, and J. Vleugels. Realistic input models for geometric algorithms. Algorithmica, 34(1) (2002), 81--97.
[5]
P. Carmi. Approximation Algorithms for Geometric Problems in Wireless Communication Networks. Ph.D. Thesis, Ben-Gurion University, March 2006.
[6]
P. Carmi, S. Dolev, S. Har-Peled, M.J. Katz, and M. Segal. Geographic quorum system approximations. Algorithmica, 41(4) (2005), 233--244.
[7]
P. Carmi, S. Har-Peled, and M.J. Katz, On the Fermat-Weber center of a convex object. Comput. Geom. Theory Appl., 32(3) (2005), 188--195.
[8]
J. Chuzhoy and Y. Rabani. Approximating k-Median with Non-Uniform Capacities. Proc. 16th ACM-SIAM Symp. Discrete Algorithms, pages 952--958, 2005.
[9]
S.P. Fekete, J.S.B. Mitchell, and K. Beurer. On the continuous Fermat-Weber problems. Operations Research, 53(1) (2005), 61--76.
[10]
H.W. Kuhn. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2 (1955), 83--97.
[11]
D.B. West. Introduction to Graph Theory. Second edition, Prentice Hall, 2001.

Cited By

View all
  • (2013)Balancing workloads of service vehicles over a geographic territory2013 IEEE/RSJ International Conference on Intelligent Robots and Systems10.1109/IROS.2013.6696355(209-216)Online publication date: Nov-2013
  • (2010)Coverage Optimization and Spatial Load Balancing by Robotic Sensor NetworksIEEE Transactions on Automatic Control10.1109/TAC.2010.204049555:3(749-754)Online publication date: Mar-2010
  • (2010)Equal-area locus-based convex polygon decompositionTheoretical Computer Science10.1016/j.tcs.2010.01.012411:14-15(1648-1667)Online publication date: 1-Mar-2010
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SCG '06: Proceedings of the twenty-second annual symposium on Computational geometry
June 2006
500 pages
ISBN:1595933409
DOI:10.1145/1137856
  • Program Chairs:
  • Nina Amenta,
  • Otfried Cheong
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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 June 2006

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. additive-weighted Voronoi diagrams
  2. approximation algorithms
  3. fat partitions
  4. fatness
  5. geometric optimization
  6. load balancing

Qualifiers

  • Article

Conference

SoCG06

Acceptance Rates

Overall Acceptance Rate 625 of 1,685 submissions, 37%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)27
  • Downloads (Last 6 weeks)18
Reflects downloads up to 12 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2013)Balancing workloads of service vehicles over a geographic territory2013 IEEE/RSJ International Conference on Intelligent Robots and Systems10.1109/IROS.2013.6696355(209-216)Online publication date: Nov-2013
  • (2010)Coverage Optimization and Spatial Load Balancing by Robotic Sensor NetworksIEEE Transactions on Automatic Control10.1109/TAC.2010.204049555:3(749-754)Online publication date: Mar-2010
  • (2010)Equal-area locus-based convex polygon decompositionTheoretical Computer Science10.1016/j.tcs.2010.01.012411:14-15(1648-1667)Online publication date: 1-Mar-2010
  • (2009)Improved bounds on the average distance to the Fermat--Weber center of a convex objectInformation Processing Letters10.1016/j.ipl.2008.11.009109:6(329-333)Online publication date: 20-Feb-2009
  • (2008)Area-constrained coverage optimization by robotic sensor networks2008 47th IEEE Conference on Decision and Control10.1109/CDC.2008.4738883(1018-1023)Online publication date: Dec-2008
  • (2008)Equal-Area Locus-Based Convex Polygon DecompositionProceedings of the 15th international colloquium on Structural Information and Communication Complexity10.1007/978-3-540-69355-0_13(141-155)Online publication date: 17-Jun-2008
  • (2007)Minimum-Cost Load-Balancing PartitionsAlgorithmica10.1007/s00453-007-9125-354:3(318-336)Online publication date: 28-Nov-2007

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media