Nearest and farthest spatial skyline queries under multiplicative weighted Euclidean distances

Abstract Consider two point sets in the plane, a set of points of interest and a set of query points that is used to establish distance restrictions with respect to the set of points of interest. A nearest/farthest spatial skyline query retrieves the subset of desirable or relevant points of interest, called skyline points, such that no other point of interest is simultaneously closer to/farther from all the query points. The nearest/farthest top- k spatial skylines, are the best k nearest/farthest spatial skylines among the existent ones. All these queries find applications in decision-making support systems, facility location, crisis management and in trips or events planning. To take into account that each point of interest has a different importance, a weight is assigned to each of them and multiplicative weighted Euclidean distances are used. In this paper, we study, for the first time, the nearest and farthest spatial skyline queries when multiplicative weighted Euclidean distances are considered. We prove that most of the properties of the traditional non weighted nearest and farthest spatial skyline queries are no longer true under the weighted Euclidean distance and, consequently, the strategies used for solving non weighted spatial skyline queries are not usable in the weighted case. We present a sequential and a parallel algorithm, to be run on the CPU and on a Graphics Processing Unit, respectively, for solving nearest/farthest weighted spatial skyline queries and to extract the nearest/farthest top- k spatial skylines. We provide the time and space complexity analysis of both algorithms together with their theoretical comparison. We also have developed a simple interface to deal with weighted spatial skyline queries which allows to visualize and store in a file the obtained spatial skylines. Finally, we present and discuss experimental results obtained with the implementation of the proposed sequential and parallel algorithms.

[1]  Cyrus Shahabi,et al.  Processing spatial skyline queries in both vector spaces and spatial network databases , 2009, TODS.

[2]  A. Mendes,et al.  Multi-outlet retail site location assessment , 2004 .

[3]  Juan Wang,et al.  Impact of individual difference and investment heterogeneity on the collective cooperation in the spatial public goods game , 2017, Knowl. Based Syst..

[4]  T. Drezner.  Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model , 1994 .

[5]  B. Boots,et al.  Modeling retail trade areas using higher-order, multiplicatively weighted voronoi diagrams , 1997 .

[6]  Jian Pei,et al.  Efficient Skyline and Top-k Retrieval in Subspaces , 2007, IEEE Transactions on Knowledge and Data Engineering.

[7]  Zou Peng,et al.  Continuous Dynamic Skyline Queries over Data Stream , 2011 .

[8]  Bernhard Seeger,et al.  Progressive skyline computation in database systems , 2005, TODS.

[9]  Seung-won Hwang,et al.  The Farthest Spatial Skyline Queries , 2013, Inf. Syst..

[10]  Gang Chen,et al.  On efficient reverse skyline query processing , 2014, Expert Syst. Appl..

[11]  Joan Antoni Sellarès,et al.  Common influence region problems , 2015, Inf. Sci..

[12]  Seung-won Hwang,et al.  MSSQ: Manhattan Spatial Skyline Queries , 2014, Inf. Syst..

[13]  Gang Chen,et al.  Efficient algorithms for finding the most desirable skyline objects , 2015, Knowl. Based Syst..

[14]  Joan Antoni Sellarès,et al.  Solving the k-influence region problem with the GPU , 2014, Inf. Sci..

[15]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[16]  Joan Antoni Sellarès,et al.  Finding influential location regions based on reverse k-neighbor queries , 2013, Knowl. Based Syst..

[17]  Man Lung Yiu,et al.  Multi-dimensional top-k dominating queries , 2009, The VLDB Journal.

[18]  David Taniar,et al.  Social-Aware Spatial Top-k and Skyline Queries , 2018, Comput. J..

[19]  Ling Liu,et al.  Multi-criteria decision making with skyline computation , 2012, 2012 IEEE 13th International Conference on Information Reuse & Integration (IRI).

[20]  Franz Aurenhammer,et al.  An optimal algorithm for constructing the weighted voronoi diagram in the plane , 1984, Pattern Recognit..

[21]  Kyuseok Shim,et al.  Parallel Computation of Skyline and Reverse Skyline Queries Using MapReduce , 2013, Proc. VLDB Endow..

[22]  Guoyin Wang,et al.  Finding strongly connected components of simple digraphs based on generalized rough sets theory , 2018, Knowl. Based Syst..

[23]  Joan Antoni Sellarès,et al.  Efficient multiple bichromatic mutual nearest neighbor query processing , 2016, Inf. Syst..

[24]  Yunjun Gao,et al.  Top-k Dominating Queries on Incomplete Data , 2016, IEEE Trans. Knowl. Data Eng..

[25]  Seung-won Hwang,et al.  Spatial skyline queries: exact and approximation algorithms , 2011, GeoInformatica.

[26]  Benjin Zhu,et al.  Improving user recommendation by extracting social topics and interest topics of users in uni-directional social networks , 2018, Knowl. Based Syst..

[27]  Joan Antoni Sellarès,et al.  Solving multiple kth smallest dissimilarity queries for non-metric dissimilarities with the GPU , 2016, Inf. Sci..

[28]  Nasrin Mazaheri Soudani,et al.  The Spatial Nearest Neighbor Skyline Queries , 2011, ArXiv.

[29]  Xuemin Lin,et al.  Efficient general spatial skyline computation , 2012, World Wide Web.

[30]  Jun-Ki Min,et al.  Spatial skyline queries over incomplete data for smart cities , 2018, J. Syst. Archit..

[31]  Zvi Drezner,et al.  Validating the Gravity-Based Competitive Location Model Using Inferred Attractiveness , 2002, Ann. Oper. Res..

[32]  Hee-Kap Ahn,et al.  Top-k Manhattan Spatial Skyline Queries , 2014, WALCOM.