New Approaches for the Point-feature Cartographic Label Placement Problem

The point-feature cartographic label placement problem (PFCLP) consists in placing text labels adjacent to point features on a map. This paper proposes a 0-1 integer linear programming model for the PFCLP defined as the maximum number of free labels placed where all points must be labeled. We also present a Lagrangean decomposition technique based on graph partitioning where the PFCLP is represented by a conflict graph and partitioned into clusters. After the partitioning phase, some variables are copied to reduce de number of inter-clusters edges and the equality constraints associated to those variables copied are relaxed in a Lagrangean way. Computational experiments for sets of 25 instances with up to 1000 points showed that our Lagrangean decomposition provides good solutions better than CPLEX and the ones reported in the literature. We optimally solved all instances up to 750 points and the optimal was proven for 5 instances with 1000 points.