Computational Statistics

, Volume 29, Issue 3–4, pp 799–811 | Cite as

Fast algorithms for a space-time concordance measure

  • Sergio J. ReyEmail author
Original Paper


This paper presents a number of algorithms for a recently developed measure of space-time concordance. Based on a spatially explicit version of Kendall’s \(\tau \) the original implementation of the concordance measure relied on a brute force \(O(n^2)\) algorithm which has limited its use to modest sized problems. Several new algorithms have been devised which move this run time to \(O(n log(n) +np)\) where \(p\) is the expected number of spatial neighbors for each unit. Comparative timing of these alternative implementations reveals dramatic efficiency gains in moving away from the brute force algorithms. A tree-based implementation of the spatial concordance is also found to dominate a merge sort implementation.


Spatial concordance Autocorrelation Rank correlation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Arizona State UniversityTempeUSA

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