![](bga.png)
5 CONCLUSIONS AND FUTURE
WORK
Processing of GNNQs has been based on index struc-
tures, so far. In this paper, for the first time, we
present new PS algorithms that can be efficiently ap-
plied on RAM-based data for processing the GNNQ.
As the experimentation that we performed, using syn-
thetic and real data sets, shows the use of median (in
GNNPS) and, even more, the use of median and cen-
troid (in GNNPSC), prunes the number of points in-
volved in processing and the number of calculations.
Although, in this paper, we do not present a com-
parison of our algorithms with respect to the algo-
rithms presented in (Papadias et al., 2004), compar-
ing the results that we have presented to the results of
(Papadias et al., 2004) for data sets of similar size (ap-
proximately 24.5K and 192/195K points) we observe
that our algorithms achieve competitive performance.
This is an initial observation. A detailed compari-
son could be performed in the future, using the same
data sets on the same machine. Moreover, the algo-
rithms we present could be transformed / extended to
work on high volume, disk resident data that are trans-
ferred in RAM in blocks. Moreover, the application
of Plane-Sweep to other spatial queries (like Reverse
NNQ) could lead to interesting techniques.
ACKNOWLEDGEMENTS
Work supported by the GENCENG project (SYN-
ERGASIA 2011 action, supported by the Euro-
pean Regional Development Fund and Greek Na-
tional Funds); project number 11SYN 8 1213. Work
also supported by the MINECO research project
[TIN2013-41576-R] and the Junta de Andaluc
´
ıa re-
search project [P10-TIC-6114].
REFERENCES
Ahn, H., Bae, S. W., and Son, W. (2013). Group nearest
neighbor queries in the L
1
plane. In TAMC Confer-
ence, pages 52–61. Springer.
Hashem, T., Kulik, L., and Zhang, R. (2010). Privacy
preserving group nearest neighbor queries. In EDBT
Conference, pages 489–500. ACM.
Hinrichs, K., Nievergelt, J., and Schorn, P. (1988). Plane-
sweep solves the closest pair problem elegantly. In-
formation Processing Letters, 26(5):255–261.
Jacox, E. H. and Samet, H. (2007). Spatial join techniques.
ACM Trans. Database Syst., 32(1):7.
Jiang, T., Gao, Y., Zhang, B., Liu, Q., and Chen, L.
(2013). Reverse top-k group nearest neighbor search.
In WAIM Conference, pages 429–439. Springer.
Li, H., Lu, H., Huang, B., and Huang, Z. (2005).
Two ellipse-based pruning methods for group near-
est neighbor queries. In ACM-GIS Conference, pages
192–199. ACM.
Li, J., Wang, B., Wang, G., and Bi, X. (2014). Efficient pro-
cessing of probabilistic group nearest neighbor query
on uncertain data. In DASFAA Conference, pages 436–
450. Springer.
Lian, X. and Chen, L. (2008). Probabilistic group nearest
neighbor queries in uncertain databases. IEEE Trans.
Knowl. Data Eng., 20(6):809–824.
Luo, Y., Chen, H., Furuse, K., and Ohbo, N. (2007). Ef-
ficient methods in finding aggregate nearest neighbor
by projection-based filtering. In ICCSA Conference,
pages 821–833. Springer.
Namnandorj, S., Chen, H., Furuse, K., and Ohbo, N. (2008).
Efficient bounds in finding aggregate nearest neigh-
bors. In DEXA Conference, pages 693–700. Springer.
Papadias, D., Shen, Q., Tao, Y., and Mouratidis, K. (2004).
Group nearest neighbor queries. In ICDE Conference,
pages 301–312. IEEE.
Papadias, D., Tao, Y., Mouratidis, K., and Hui, C. K.
(2005). Aggregate nearest neighbor queries in spatial
databases. ACM Trans. Database Syst., 30(2):529–
576.
Preparata, F. P. and Shamos, M. I. (1985). Computational
Geometry - An Introduction. Springer, New York, NY.
Rigaux, P., Scholl, M., and Voisard, A. (2002). Spatial
databases - with applications to GIS. Elsevier, San
Francisco, CA.
Roumelis, G., Vassilakopoulos, M., Corral, A., and
Manolopoulos, Y. (2014). A new plane-sweep algo-
rithm for the k-closest-pairs query. In SOFSEM Con-
ference, pages 478–490. Springer.
Zhang, D., Chan, C., and Tan, K. (2013). Nearest group
queries. In SSDBM Conference, page 7. ACM.
Zhu, L., Jing, Y., Sun, W., Mao, D., and Liu, P. (2010).
Voronoi-based aggregate nearest neighbor query pro-
cessing in road networks. In ACM-GIS Conference,
pages 518–521. ACM.
APPENDIX
Lemma: The sum of dx-distances between one given
point p(x,y) ∈ P and all points of the query set Q
(sumdx(p, Q)):
A Is minimized at the median point q[m] (where q[m]
is the array notation of q
m
),
B For all p.x ≥ q[m].x, sumdx is constant or increas-
ing with the increment of x, and
C For all p.x < q[m].x, sumdx is increasing while x
decreases.
GISTAM2015-1stInternationalConferenceonGeographicalInformationSystemsTheory,ApplicationsandManagement
92