Geodesic
Mass updates on multidimensional data
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 99-100 
A. G. Bannykh. Mass updates on multidimensional data. Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 99-100. http://geodesic.mathdoc.fr/item/PDMA_2012_5_a52/
@article{PDMA_2012_5_a52,
     author = {A. G. Bannykh},
     title = {Mass updates on multidimensional data},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {99--100},
     year = {2012},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2012_5_a52/}
}
TY  - JOUR
AU  - A. G. Bannykh
TI  - Mass updates on multidimensional data
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2012
SP  - 99
EP  - 100
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/PDMA_2012_5_a52/
LA  - ru
ID  - PDMA_2012_5_a52
ER  - 
%0 Journal Article
%A A. G. Bannykh
%T Mass updates on multidimensional data
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2012
%P 99-100
%N 5
%U http://geodesic.mathdoc.fr/item/PDMA_2012_5_a52/
%G ru
%F PDMA_2012_5_a52

Voir la notice de l'article provenant de la source Math-Net.Ru

A problem of efficient implementation of mass updates on multidimensional data is studied. For a specific range of operations, a flexible solution is proposed. The solution is applicable if the data elements form an abelian group with some operator $+$. In that case, the proposed method allows effective sum calculation and addition of the same value to the rectangular areas.

[1] Romanovskii I. V., Diskretnyi analiz, Nevskii Dialekt, BKhV-Peterburg, SPb., 2008, 336 pp.

[2] Bentley J. L., “Multidimensional binary search trees used for associative searching”, Commun. ACM, 18:9 (1975), 509–517 | DOI | MR | Zbl

[3] Preparata F., Sheimos M., Vychislitelnaya geometriya. Vvedenie, Mir, M., 1989, 478 pp. | MR | Zbl

[4] Fenwick P. M., “A New Data Structure for Cumulative Frequency Tables”, Software: Practice and Experience, 24:3 (1994), 327–336 | DOI

[5] Bannykh A. G., Primenenie derevev dlya realizatsii massovykh operatsii na mnogomernykh massivakh dannykh, [Elektronnyi resurs] , 2011 http://is.ifmo.ru/papers/2011-bachelor-bannykh/