Column generation approach for the point-feature cartographic label placement problem

Ribeiro, Glaydston Mattos; Lorena, Luiz Antônio Nogueira

doi:10.1007/s10878-007-9073-5

Cited by 10 publications

(10 citation statements)

References 24 publications

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“…The model (1)-(4) is similar to the one proposed by Zoraster [5] and Ribeiro and Lorena [9] but it allows allocating all labels maximizing the number of conflict free labels. Fig.…”

Section: The Proposed Modelmentioning

confidence: 99%

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A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem

Mauri

Ribeiro

Lorena

2010

Computers & Operations Research

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a b s t r a c tThis paper proposes a 0-1 integer linear programming model for the point-feature cartographic label placement problem based on labeling of the largest number of free labels. In addition, one non-trivial valid inequality is presented to strengthen this proposed model. Even with the strengthened model, a commercial solver was not able to solve a representative sample of known instances presented in the literature. Thus, we also present a Lagrangean decomposition technique based on graph partitioning. Our added approaches established optimal solutions for practically all the used instances and the results significantly improved the ones presented in recent studies concerning the problem.

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“…The model (1)-(4) is similar to the one proposed by Zoraster [5] and Ribeiro and Lorena [9] but it allows allocating all labels maximizing the number of conflict free labels. Fig.…”

Section: The Proposed Modelmentioning

confidence: 99%

“…The MNCFLP [6] is also known as the label overlap minimization problem [7] and the number of labels obstructed by at least one other label [8]. The MNCP was recently presented by Ribeiro and Lorena [6,9] and this approach ''spread'' the overlaps to minimize conflicts (edges) between candidate positions.…”

Section: Introductionmentioning

confidence: 99%

A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem

Mauri

Ribeiro

Lorena

2010

Computers & Operations Research

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“…Ribeiro and Lorena (2008a) proposed a Lagrangean Relaxation with Clusters (LagClus) for point labeling with Minimum Number of Conflicts. The approach presented by the authors is as follows.…”

Section: Lagrangean Decompositionmentioning

confidence: 99%

“…Our decomposition is based on the idea presented by Ribeiro and Lorena (2008a), however, instead of relaxing all constraints with vertices in different clusters, we make copies of the decision variables to include them into the sub-problems, and relax those necessary additional constraints to make sure that the original variables and the copies are equal. This approach reduces the number of constraints to be relaxed, providing a Lagrangean relaxation stronger than the one proposed by Ribeiro and Lorena (2008a).…”

Section: Lagrangean Decompositionmentioning

confidence: 99%

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A lagrangean decomposition for the maximum independent set problem applied to map labeling

2010

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The Maximum Independent Set (MIS) problem is a well-known problem where the aim is to find the maximum cardinality independent set in an associated graph. Map labeling problems can often be modeled as a MIS problem in a conflict graph, where labels are selected to be placed near graphical features not allowing overlaps (conflicts) between labels or between labels and features. However, the MIS problem is NP-hard and exact techniques present difficulties for solving some instances. Thus, this paper presents a Lagrangean decomposition to solve a map labeling problem, the Point-Feature Label Placement problem. We treated the problem by a conflict graph that is partitioned into small sub-problems and copies of some decision variables are done. These copies are used in the subproblems constraints and in some constraints to ensure the equality between the original variables and their copies. After these steps, we relax these copy constraints in a Lagrangean way. Using instances proposed in the literature, our approach was able to prove the optimality for all of them, except one, and the results were better than the ones provided by a commercial solver.

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A two-phase algorithm for point-feature cartographic label placement

Ding

Jiang

et al. 2017

Earth Sci Inform

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Column generation approach for the point-feature cartographic label placement problem

Abstract: This paper proposes a column generation approach for the Point-Feature Cartographic Label Placement problem (PFCLP)

Cited by 10 publications

References 24 publications

A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem

A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem

A lagrangean decomposition for the maximum independent set problem applied to map labeling

A two-phase algorithm for point-feature cartographic label placement

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