An overlapping Voronoi diagram-based system for multi-criteria optimal location queries

This paper presents a novel Multi-criteria Optimal Location Query (MOLQ), which can be applied to a wide range of applications. After providing a formal definition of the novel query type, we propose an Overlapping Voronoi Diagram (OVD) model that defines OVDs and Minimum OVDs (MOVDs), and an OVD overlap operation. Based on the OVD model, we design advanced approaches to answer the query in Euclidean space. Due to the high complexity of Voronoi diagram overlap computation, we improve the overlap operation by replacing the real boundaries of Voronoi diagrams with their Minimum Bounding Rectangles (MBR). Moreover, if there are changes to a limited number of objects, re-evaluating queries over updated object sets would be expensive. Thus, we also propose an MOVD updating model and an advanced algorithm to incrementally update MOVDs to avoid the high cost of query re-evaluation. Our experimental results show that the proposed algorithms can evaluate the novel query type effectively and efficiently.

[1]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[2]  Yufei Tao,et al.  Multi-dimensional Reverse k NN Search , 2005 .

[3]  David Simmonds,et al.  Residential Location Choice , 2010 .

[4]  Yufei Tao,et al.  Multidimensional reverse kNN search , 2007, The VLDB Journal.

[5]  Cun-Hui Zhang,et al.  A modified Weiszfeld algorithm for the Fermat-Weber location problem , 2001, Math. Program..

[6]  J. Shane Culpepper,et al.  Maximizing Bichromatic Reverse Spatial and Textual k Nearest Neighbor Queries , 2016, Proc. VLDB Endow..

[7]  Yufei Tao,et al.  Reverse kNN Search in Arbitrary Dimensionality , 2004, VLDB.

[8]  Dan Lin,et al.  The Min-dist Location Selection Query , 2012, 2012 IEEE 28th International Conference on Data Engineering.

[9]  Olivier Devillers.  On Deletion in Delaunay Triangulations , 2002, Int. J. Comput. Geom. Appl..

[10]  Muhammad Aamir Cheema,et al.  Continuous reverse k nearest neighbors queries in Euclidean space and in spatial networks , 2011, The VLDB Journal.

[11]  J. Haldane.  Note on the median of a multivariate distribution , 1948 .

[12]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[13]  Feifei Li,et al.  Optimal location queries in road network databases , 2011, 2011 IEEE 27th International Conference on Data Engineering.

[14]  Arie Tamir,et al.  Algebraic optimization: The Fermat-Weber location problem , 1990, Math. Program..

[15]  Xiao Qin,et al.  Multi-Criteria Optimal Location Query with Overlapping Voronoi Diagrams , 2014, EDBT.

[16]  Yunjun Gao,et al.  Optimal-Location-Selection Query Processing in Spatial Databases , 2009, IEEE Transactions on Knowledge and Data Engineering.

[17]  King-Ip Lin,et al.  An index structure for efficient reverse nearest neighbor queries , 2001, Proceedings 17th International Conference on Data Engineering.

[18]  Kazuo Murota,et al.  IMPROVEMENTS OF THE INCREMENTAL METHOD FOR THE VORONOI DIAGRAM WITH COMPUTATIONAL COMPARISON OF VARIOUS ALGORITHMS , 1984 .

[19]  Xiao Qin,et al.  A framework for multi-criteria optimal location selection , 2015, SIGSPATIAL/GIS.

[20]  Ugur Demiryurek,et al.  Indexing Network Voronoi Diagrams , 2012, DASFAA.

[21]  Lan Mu.  Polygon Characterization With the Multiplicatively Weighted Voronoi Diagram* , 2004, The Professional Geographer.

[22]  Yubao Liu,et al.  Finding multiple new optimal locations in a road network , 2016, SIGSPATIAL/GIS.

[23]  Ji Zhang,et al.  A framework for updating multi-criteria optimal location query (demo paper) , 2016, SIGSPATIAL/GIS.

[24]  Mariette Yvinec,et al.  Dynamic Additively Weighted Voronoi Diagrams in 2D , 2002, ESA.

[25]  Farnoush Banaei Kashani,et al.  Continuous maximal reverse nearest neighbor query on spatial networks , 2012, SIGSPATIAL/GIS.

[26]  Pinliang Dong,et al.  Generating and updating multiplicatively weighted Voronoi diagrams for point, line and polygon features in GIS , 2008, Comput. Geosci..

[27]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[28]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[29]  Yufei Tao,et al.  Reverse Nearest Neighbor Search in Metric Spaces , 2006, IEEE Transactions on Knowledge and Data Engineering.

[30]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[31]  Chandrajit L. Bajaj,et al.  The algebraic degree of geometric optimization problems , 1988, Discret. Comput. Geom..

[32]  Feifei Li,et al.  Dynamic monitoring of optimal locations in road network databases , 2013, The VLDB Journal.

[33]  Jakob Krarup,et al.  Geometrical Solution to the Fermat Problem with Arbitrary Weights , 2003, Ann. Oper. Res..

[34]  Divesh Srivastava,et al.  Reverse Nearest Neighbor Aggregates Over Data Streams , 2002, VLDB.

[35]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[36]  S. Muthukrishnan,et al.  Influence sets based on reverse nearest neighbor queries , 2000, SIGMOD '00.

[37]  M. Iri,et al.  Construction of the Voronoi diagram for 'one million' generators in single-precision arithmetic , 1992, Proc. IEEE.

[38]  Ulrich Finke,et al.  Overlaying simply connected planar subdivisions in linear time , 1995, SCG '95.

[39]  Yang Du,et al.  On Computing Top-t Most Influential Spatial Sites , 2005, VLDB.

[40]  M. Ben-Akiva,et al.  Tradeoffs in residential location decisions: Transportation versus other factors , 1980 .

[41]  Steven Fortune,et al.  Numerical stability of algorithms for 2D Delaunay triangulations , 1992, SCG '92.

[42]  Yufei Tao,et al.  Reverse nearest neighbors in large graphs , 2005, 21st International Conference on Data Engineering (ICDE'05).

[43]  Frank Plastria,et al.  On the point for which the sum of the distances to n given points is minimum , 2009, Ann. Oper. Res..

[44]  Margarida Mamede,et al.  Updates on Voronoi Diagrams , 2011, 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering.

[45]  David Simmonds,et al.  Residential Location Choice - Models and Applications , 2010 .

[46]  Cheng Long,et al.  Efficient algorithms for optimal location queries in road networks , 2014, SIGMOD Conference.

[47]  Divyakant Agrawal,et al.  Discovery of Influence Sets in Frequently Updated Databases , 2001, VLDB.

[48]  Franz Aurenhammer,et al.  Voronoi Diagrams and Delaunay Triangulations , 2013 .

[49]  Yufei Tao,et al.  Progressive computation of the min-dist optimal-location query , 2006, VLDB.

[50]  Boris S. Verkhovsky,et al.  Feedback Algorithm for the Single-Facility Minisum Problem , 2003 .

[51]  George O. Wesolowsky,et al.  FACILITIES LOCATION: MODELS AND METHODS , 1988 .

[52]  Leonidas J. Guibas,et al.  Randomized incremental construction of Delaunay and Voronoi diagrams , 1990, Algorithmica.

[53]  C. Gold,et al.  Delete and insert operations in Voronoi/Delaunay methods and applications , 2003 .

[54]  Robert F. Love,et al.  A generalization of the rectangular bounding method for continuous location models , 2002 .

[55]  Yang Du,et al.  The Optimal-Location Query , 2005, SSTD.

[56]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[57]  Jean-Daniel Boissonnat,et al.  Convex Hull and Voronoi Diagram of Additively Weighted Points , 2005, ESA.