Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves
A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2003-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3338/pdf |
| _version_ | 1797270647746854912 |
|---|---|
| author | Ho-Kwok Dai Hung-Chi Su |
| author_facet | Ho-Kwok Dai Hung-Chi Su |
| author_sort | Ho-Kwok Dai |
| collection | DOAJ |
| description | A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics. |
| first_indexed | 2024-04-25T02:07:36Z |
| format | Article |
| id | doaj.art-ba6e3908b0bd4947a35a9ba09985540d |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:07:36Z |
| publishDate | 2003-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-ba6e3908b0bd4947a35a9ba09985540d2024-03-07T14:29:56ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502003-01-01DMTCS Proceedings vol. AC,...Proceedings10.46298/dmtcs.33383338Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling CurvesHo-Kwok Dai0Hung-Chi Su1Computer Science Department- University of OklahomaComputer Science - ArkansasA discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.https://dmtcs.episciences.org/3338/pdfspace-filling curveshilbert curvesz-order curvesclusteringrandom walk[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| spellingShingle | Ho-Kwok Dai Hung-Chi Su Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves Discrete Mathematics & Theoretical Computer Science space-filling curves hilbert curves z-order curves clustering random walk [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| title | Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves |
| title_full | Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves |
| title_fullStr | Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves |
| title_full_unstemmed | Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves |
| title_short | Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves |
| title_sort | approximation and analytical studies of inter clustering performances of space filling curves |
| topic | space-filling curves hilbert curves z-order curves clustering random walk [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| url | https://dmtcs.episciences.org/3338/pdf |
| work_keys_str_mv | AT hokwokdai approximationandanalyticalstudiesofinterclusteringperformancesofspacefillingcurves AT hungchisu approximationandanalyticalstudiesofinterclusteringperformancesofspacefillingcurves |