Article

Free access

Clustering algorithms based on minimum and maximum spanning trees

Authors:

T. Asano,

B. Bhattacharya,

M. Keil,

F. YaoAuthors Info & Claims

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

Pages 252 - 257

https://doi.org/10.1145/73393.73419

Published: 06 January 1988 Publication History

PDF eReader

Abstract

We consider clustering problems under two different optimization criteria. One is to minimize the maximum intracluster distance (diameter), and the other is to maximize the minimum intercluster distance. In particular, we present an algorithm which partitions a set S of n points in the plane into two subsets so that their larger diameter is minimized in time Ο(n log n) and space Ο(n). Another algorithm with the same bounds computes a k-partition of S for any k so that the minimum intercluster distance is maximized. In both instances it is first shown that an optimal parition is determined by either a maximum or minimum spanning tree of S.

References

[1]

A. Aho, J. Hopcroft and J. UUman, The Design and Analysis of Computei" Algorithms, Addison-Wesley, Reading, Mass., 1974.

Digital Library

Google Scholar

[2]

D. Avis, Diameter Partitioning, Discrete and Computational Geometry, 1, 1986, 265-276.

Digital Library

Google Scholar

[3]

P. Brucker, On the Complexity of Clustering Problems, in R. Henn, B. Korte and W. Oletti, eds., Optimizing and Operations Research, Springer, Berlin, 1977.

Google Scholar

[4]

H. Edelsbrunner, H. A. Maurer, F. P. Preparata, A. L. Rosenberg, E. Welzl and D. Wood, Stabbing Line Segments, BIT, 22, 1982, 274-281.

Google Scholar

[5]

T. Gonzalez, Algorithms on Sets and Related Problems, Technical Keport, Computer Science Department, University of Oklahoma, 197'5.

Google Scholar

[6]

J. A. tIartingan, Clustering Algorithms, John-Wiley, New York, 1975.

Digital Library

Google Scholar

[7]

D.S. Johnson, The NP-Completeness Column: An Ongoing Guide, Journal of Algorithms, 3, 1982, 182-195.

Digital Library

Google Scholar

[8]

U. Manber and M. Tompa, Probabilistic, Nondeterministic and Alternating Decision Trees, Tit No. 82-03-01, University of Washington, 1982.

Google Scholar

[9]

C. Monma, M. Paterson, S. Suri and F. Yao, Computing Euclidean Maximum Spanning Trees, these proceedings.

Digital Library

Google Scholar

[10]

F.P. Preparata and M. I. Shamos, Computational Geometry, 1, Springer Verlag, New York, NY, 1985.

Digital Library

Google Scholar

Cited By

View all

Aydın Nİşseven T(2024)Gravity modelling by using vertical prismatic polyhedra and application to a sedimentary basin in Eastern AnatoliaNear Surface Geophysics10.1002/nsg.1229722:3(383-401)Online publication date: 28-Mar-2024
https://doi.org/10.1002/nsg.12297
Correddu MTrevisan D(2023)On minimum spanning trees for random Euclidean bipartite graphsCombinatorics, Probability and Computing10.1017/S0963548323000445(1-32)Online publication date: 30-Nov-2023
https://doi.org/10.1017/S0963548323000445
Yang QGao WHan GLi ZTian MZhu SDeng Y(2023)HCDCInformation Systems10.1016/j.is.2022.102159114:COnline publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.is.2022.102159
Show More Cited By

Recommendations

On the maximum degree of minimum spanning trees
SCG '94: Proceedings of the tenth annual symposium on Computational geometry

Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the L_p norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ...
Minimum restricted diameter spanning trees

Let G = (V,E) be a requirement graph. Let d = (d_ij)ⁿ_i,j=1 be a length metric. For a tree T denote by d_T(i,j) the distance between i and j in T (the length according to d of the unique i - j path in T). The restricted diameter of T, D_T, is the maximum ...
Minimum Restricted Diameter Spanning Trees
APPROX '02: Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization

Let G = ( V, E ) be a requirements graph. Let d = ( d _ij ) _i,j=1 ⁿ be a length metric. For a tree T denote by d _T ( i,j ) the distance between i and j in T (the length according to d of the unique i - j path in T ). The ...

Comments

Information & Contributors

Information

Published In

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

January 1988

403 pages

ISBN:0897912705

DOI:10.1145/73393

Chairman:
H. Edelsbrunner
Univ. of Illinois, Urbana-Champaign

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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 January 1988

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

CG88

Sponsor:

SIGACT

CG88: Symposium on Computational Geometery

June 6 - 8, 1988

Illinois, Urbana-Champaign, USA

Acceptance Rates

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

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

80
Total Citations
View Citations
2,087
Total Downloads

Downloads (Last 12 months)131
Downloads (Last 6 weeks)11

Reflects downloads up to 02 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Aydın Nİşseven T(2024)Gravity modelling by using vertical prismatic polyhedra and application to a sedimentary basin in Eastern AnatoliaNear Surface Geophysics10.1002/nsg.1229722:3(383-401)Online publication date: 28-Mar-2024
https://doi.org/10.1002/nsg.12297
Correddu MTrevisan D(2023)On minimum spanning trees for random Euclidean bipartite graphsCombinatorics, Probability and Computing10.1017/S0963548323000445(1-32)Online publication date: 30-Nov-2023
https://doi.org/10.1017/S0963548323000445
Yang QGao WHan GLi ZTian MZhu SDeng Y(2023)HCDCInformation Systems10.1016/j.is.2022.102159114:COnline publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.is.2022.102159
Jacobs B(2023)Image Trinarization Using a Partial Differential Equation: A Novel Approach to Automatic Sperm Image AnalysisApplied Mathematical Modelling10.1016/j.apm.2023.10.025Online publication date: Oct-2023
https://doi.org/10.1016/j.apm.2023.10.025
Maji SSadhu S(2023)Arbitrary-Oriented Color Spanning Region for Line SegmentsAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-25211-2_6(71-86)Online publication date: 26-Jan-2023
https://doi.org/10.1007/978-3-031-25211-2_6
Levin M(2022)Balanced Clustering with a Tree over ClustersJournal of Communications Technology and Electronics10.1134/S106422692113005266:S1(S23-S34)Online publication date: 24-Mar-2022
https://doi.org/10.1134/S1064226921130052
Bertrand PBroniatowski MMarcotorchino J(2022)Independence versus indetermination: basis of two canonical clustering criteriaAdvances in Data Analysis and Classification10.1007/s11634-021-00484-116:4(1069-1093)Online publication date: 8-Jan-2022
https://doi.org/10.1007/s11634-021-00484-1
Maji SSadhu S(2022)Color-Spanning Problem for Line SegmentsComputational Science and Its Applications – ICCSA 202210.1007/978-3-031-10522-7_6(76-89)Online publication date: 15-Jul-2022
https://doi.org/10.1007/978-3-031-10522-7_6
Li KYuan LZhang YChen G(2021)An Accurate and Efficient Large-scale Regression Method through Best Friend ClusteringIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2021.3134336(1-1)Online publication date: 2021
https://doi.org/10.1109/TPDS.2021.3134336
Bekos MGronemann MMontecchiani FPálvölgyi DSymvonis ATheocharous L(2021)Grid drawings of graphs with constant edge-vertex resolutionComputational Geometry: Theory and Applications10.1016/j.comgeo.2021.10178998:COnline publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1016/j.comgeo.2021.101789
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

On the maximum degree of minimum spanning trees

Minimum restricted diameter spanning trees

Minimum Restricted Diameter Spanning Trees

Comments

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

PDF

eReader

Login options

Full Access

Abstract

References

Cited By

Index Terms

Recommendations

On the maximum degree of minimum spanning trees

Minimum restricted diameter spanning trees

Minimum Restricted Diameter Spanning Trees

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations