Smooth kinetic maintenance of clusters

We propose a simple, deterministic kinetic data structure (KDS) for maintaining a covering of moving points by axis-aligned unit boxes in Rd. The number of boxes is always within a factor of 3d of the best possible static covering. In the plane, this approximation factor (9) compares favorably with the approximation factor (around one million) of the best previous algorithm. The new KDS is efficient, local, compact, and responsive.

[1]  Dimitrios Gunopulos,et al.  On indexing mobile objects , 1999, PODS '99.

[2]  Leonidas J. Guibas,et al.  Geometric spanners for routing in mobile networks , 2005 .

[3]  Leonidas J. Guibas,et al.  Data structures for mobile data , 1997, SODA '97.

[4]  Stefano Basagni,et al.  Distributed clustering for ad hoc networks , 1999, Proceedings Fourth International Symposium on Parallel Architectures, Algorithms, and Networks (I-SPAN'99).

[5]  Pankaj K. Agarwal,et al.  Maintaining approximate extent measures of moving points , 2001, SODA '01.

[6]  Harry B. Hunt,et al.  NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs , 1998, J. Algorithms.

[7]  Leonidas J. Guibas,et al.  Kinetic Medians and kd-Trees , 2002, ESA.

[8]  Christian S. Jensen,et al.  Indexing the positions of continuously moving objects , 2000, SIGMOD '00.

[9]  Herbert Edelsbrunner,et al.  Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms , 1988, SCG '88.

[10]  Mario Gerla,et al.  Multicluster, mobile, multimedia radio network , 1995, Wirel. Networks.

[11]  Mahmoud Naghshineh,et al.  Bluetooth: vision, goals, and architecture , 1998, MOCO.

[12]  Sergey Bereg,et al.  Mobile facility location (extended abstract) , 2000, DIALM '00.

[13]  Sariel Har-Peled.  Clustering Motion , 2004, Discret. Comput. Geom..

[14]  Robert J. Fowler,et al.  Optimal Packing and Covering in the Plane are NP-Complete , 1981, Inf. Process. Lett..

[15]  Mary Baker,et al.  Mitigating routing misbehavior in mobile ad hoc networks , 2000, MobiCom '00.

[16]  Hans-Peter Kriegel,et al.  The R*-tree: an efficient and robust access method for points and rectangles , 1990, SIGMOD '90.

[17]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[18]  Pankaj K. Agarwal,et al.  STAR-Tree: An Efficient Self-Adjusting Index for Moving Objects , 2002, ALENEX.

[19]  Leonidas J. Guibas,et al.  Discrete Mobile Centers , 2003, Discret. Comput. Geom..

[20]  Wolfgang Maass,et al.  Approximation schemes for covering and packing problems in image processing and VLSI , 1985, JACM.

[21]  D. Eppstein,et al.  Approximation algorithms for geometric problems , 1996 .