A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation
The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of aff...
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2025-01-01
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| author | Daniel A. Griffith Yongwan Chun Hyun Kim |
| author_facet | Daniel A. Griffith Yongwan Chun Hyun Kim |
| author_sort | Daniel A. Griffith |
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| description | The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the <i>p</i> = 2 setting linkages already established for the <i>p</i> = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient <i>p</i> = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-0e6964a1f17c4981a1f2c35c23bb3d362025-01-24T13:39:53ZengMDPI AGMathematics2227-73902025-01-0113224910.3390/math13020249A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial AutocorrelationDaniel A. Griffith0Yongwan Chun1Hyun Kim2School of Economic, Political, and Policy Sciences, University of Texas at Dallas, Richardson, TX 75080, USASchool of Economic, Political, and Policy Sciences, University of Texas at Dallas, Richardson, TX 75080, USADepartment of Geography and Sustainability, University of Tennessee, Knoxville, TN 37996, USAThe existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the <i>p</i> = 2 setting linkages already established for the <i>p</i> = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient <i>p</i> = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation.https://www.mdpi.com/2227-7390/13/2/249local spatial autocorrelationmajority theoremspatial autocorrelationspatial medianspatial optimization |
| spellingShingle | Daniel A. Griffith Yongwan Chun Hyun Kim A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation Mathematics local spatial autocorrelation majority theorem spatial autocorrelation spatial median spatial optimization |
| title | A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation |
| title_full | A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation |
| title_fullStr | A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation |
| title_full_unstemmed | A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation |
| title_short | A Majority Theorem for the Uncapacitated <i>p</i> = 2 Median Problem and Local Spatial Autocorrelation |
| title_sort | majority theorem for the uncapacitated i p i 2 median problem and local spatial autocorrelation |
| topic | local spatial autocorrelation majority theorem spatial autocorrelation spatial median spatial optimization |
| url | https://www.mdpi.com/2227-7390/13/2/249 |
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