Approximation algorithms for free-label maximization

Inspired by air-traffic control and other applications where moving objects have to be labeled, we consider the following (static) point-labeling problem: given a set P of n points in the plane and labels that are unit squares, place a label with each point in P in such a way that the number of free labels (labels not intersecting any other label) is maximized. We develop efficient constant-factor approximation algorithms for this problem, as well as PTASs, for various label-placement models.

[1]  Mohammad Ghodsi,et al.  A fast algorithm for updating a labeling to avoid a moving point , 2004, CCCG.

[2]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[3]  Subhash Suri,et al.  Label placement by maximum independent set in rectangles , 1998, CCCG.

[4]  Joe Marks,et al.  The Computational Complexity of Cartographic Label Placement , 1991 .

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

[6]  Ronald L. Rivest,et al.  Introduction to Algorithms, third edition , 2009 .

[7]  Raimund Seidel,et al.  Constructing Arrangements of Lines and Hyperplanes with Applications , 1986, SIAM J. Comput..

[8]  Martin Nöllenburg,et al.  Consistent labeling of rotating maps , 2011, J. Comput. Geom..

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

[10]  Alexander Wolff,et al.  Labeling Points with Weights , 2001, Algorithmica.

[11]  A. R. Forrest,et al.  Application Challenges to Computational Geometry: CG Impact Task Force Report , 1999 .

[12]  Alexander Wolff,et al.  Optimizing active ranges for consistent dynamic map labeling , 2008, SCG '08.

[13]  Alexander Wolff,et al.  Point labeling with sliding labels , 1999, Comput. Geom..

[14]  Frank Wagner,et al.  A packing problem with applications to lettering of maps , 1991, SCG '91.

[15]  Timothy M. Chan.  A note on maximum independent sets in rectangle intersection graphs , 2004, Inf. Process. Lett..

[16]  Alexander Wolff,et al.  Trimming of Graphs, with Application to Point Labeling , 2008, Theory of Computing Systems.

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

[18]  Parinya Chalermsook,et al.  Maximum independent set of rectangles , 2009, SODA.

[19]  Sergey Bereg,et al.  New Bounds on Map Labeling with Circular Labels , 2004, ISAAC.