Labeling collinear sites

We consider a map labeling problem, where the sites to be labeled are restricted on a line L. This is quite common e.g. in schematized maps for road or subway networks. Each site si, is associated with an axis-parallel witimeshi label li, which can be placed anywhere on the "boundary" of the input line L. The main task is to place the labels in distinct positions, so that they do not overlap and do not obscure the site set, and to connect each label with its associated site through a leader, such that no two leaders intersect. We propose several variations of this problem and we investigate their computational complexity under certain optimization criteria.

[1]  Pinhas Yoeli,et al.  The Logic of Automated Map Lettering , 1972 .

[2]  D. T. Lee,et al.  Labeling Points on a Single Line , 2005, Int. J. Comput. Geom. Appl..

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

[4]  Chengbin Chu,et al.  A survey of the state-of-the-art of common due date assignment and scheduling research , 2002, Eur. J. Oper. Res..

[5]  C.L. Yang,et al.  Single-machine scheduling to minimize the number of early jobs , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

[6]  Alexander Wolff,et al.  Labeling Subway Lines , 2001, ISAAC.

[7]  Michael A. Bekos,et al.  Polygon labelling of minimum leader length , 2006, APVIS.

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

[9]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties: A Review , 1990, Oper. Res..

[10]  Michiel H. M. Smid,et al.  Geometric Algorithms for Density-based Data Clustering , 2005, Int. J. Comput. Geom. Appl..

[11]  Robert E. Tarjan,et al.  One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties , 1988, Math. Oper. Res..

[12]  Sebastian Müller,et al.  A Smart Algorithm for Column Chart Labeling , 2005, Smart Graphics.

[13]  Steven Zoraster,et al.  The Solution of Large 0-1 Integer Programming Problems Encountered in Automated Cartography , 1990, Oper. Res..

[14]  Gur Mosheiov,et al.  Single machine scheduling to minimize the number of early and tardy jobs , 1996, Comput. Oper. Res..

[15]  Han Hoogeveen,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

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

[17]  Jean-Daniel Fekete,et al.  Excentric Labeling: Dynamic Neighborhood Labeling for Data Visualization , 2003 .

[18]  Steven Zoraster,et al.  Practical Results Using Simulated Annealing for Point Feature Label Placement , 1997 .

[19]  Alexander Wolff,et al.  Boundary labeling: Models and efficient algorithms for rectangular maps , 2004, Comput. Geom..

[20]  Michael A. Bekos,et al.  Boundary Labelling of Optimal Total Leader Length , 2005, Panhellenic Conference on Informatics.

[21]  Stephen A. Hirsch,et al.  An Algorithm for Automatic Name Placement Around Point Data , 1982 .

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

[23]  E. Imhof.  Positioning Names on Maps , 1975 .

[24]  Christos Koulamas.  Single-machine scheduling with time windows and earliness/tardiness penalties , 1996 .

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