Lagrangean relaxation with clusters for point-feature cartographic label placement problems

This paper presents two new mathematical formulations for the Point-Feature Cartographic Label Placement Problem (PFCLP ) and a new Lagrangean relaxation with clusters (LagClus) to provide bounds to these formulations. The PFCLP can be represented by a conflict graph and the relaxation divides the graph in small sub problems (clusters) that are easily solved. The edges connecting clusters are relaxed in a Lagrangean way and a subgradient algorithm improves the bounds. The LagClus was successfully applied to a set of instances up to 1000 points providing the best results of those reported in the literature.

• Type: Journal
• Year: 2008
• Where: COR
• Authors: Glaydston Mattos Ribeiro, Luiz Antonio Nogueira Lorena
• Keywords: Cartographic Label Placement, Conflict Graph, COR 2008, Small Sub Problems