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Fast Point-Feature Label Placement Algorithm for Real Time Screen Maps Missae Yamamoto Gilberto Camara Luiz Antonio Nogueira Lorena

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Schedule Definition Label placement potential label positions cartographic preference The combinatorial explosion of possible solutions Conflict graph and adjacency matrix FALP - Fast Algorithm for Label Placement Results Sample of label placement for 1000 points Conclusion

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Label placement (FONTE: Edmondson et. al. (1996, p. 14).

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The label placement problem We want our maps to be legible Name placement can be one of the most time- consuming aspects of map production, Names must not overlap Names must be clearly associated with the features they annotate

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A good map must be easily readable Source: ESRI

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Why fast algorithms for label placement? Web maps are very popular Map servers allow the user to combine many layers Layers have text associated Unfeasible to pre-compute all label arrangements We need fast ways to generate good quality maps for web map servers

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Source: Institute for Cartography and Geoinformation, University of Bonn

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A set of potential label positions and their cartographic preference (best = 1; worse = 4)

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the combinatorial explosion of possible solutions P1/L0P1/L1 P2/L1P2/L0 P2/L1 P3/L1P3/L0P3/L1P3/L0 1 point 2¹ configurations 2 points 2² configurations 3 points 2³ configurations 1000 points 2¹ººº configurations L0 L1

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Two points – potential label positions and corresponding conflict graph Candidate label positionsConflict graph (linked nodes have conflicts)

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A conflict graph as an adjacency matrix Number of conflicts (node degree): L5 = 4

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Fast Algorithm for Label Placement (FALP)

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A fast algorithm for label placement Create the conflict graph (done off-line). Use the conflict graph to label as many points as possible. Create a labeling for the remaining points Use local search to improve map quality.

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The maximum nonconflict labeling algorithm ( Uses the conflict graph to label as many points as possible.)

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Example of label arrangement

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Adjacency matrix for example

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Label with least conflicts is L24 Solution1 = {(P6, L24)}

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Label with least conflicts is L02 Solution 2 = {(P6, L24), (P1, L02)}

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Label with least conflicts is L05 Solution3 = {( P6, L24), (P1, L02), (P2, L05)}

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Two labels with 4 conflicts (L12 or L18) P3 = {L11, L12 } or P5 = {L18, L19, L20}? We choose {P3, L12} since P3 has two possible label positions and P5 has three

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Label with least conflicts is L12 Solution4 = {( P6, L24), (P1, L02), (P2, L05), (P3, L12)}

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Label with least conflicts is L15 S= {( P6, L24), (P1, L02), (P2, L05), (P3, L12), (P4, L15)}

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Remaining label is L18 final solution S= {( P6, L24), (P1, L02), (P2, L05), (P3, L12), (P4, L15), (P5, L18)}

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Processing labels with conflicts (Create a labeling for the remaining points)

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Processing of labels with conflicts S * = {(P1, L02), (P2, L05), (P3, 0), (P4, L14), (P5, 0), (P6, L23)} Point P3 has candidate labels L = {(L09, 1), (L10, 2), (L11, 1), (L12,0)} S* = {(P1, L02), (P2, L05), (P3, L12), (P4, L14), (P5, 0), (P6, L23)} Point P5 has candidate labels L= {(L17, 3), (L18, 1), (L19, 1), (L20, 2)} S* = {(P1, L02), (P2, L05), (P3, L12), (P4, L14), (P5, L18), (P6, L23)}

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Local search algorithm ( Use local search to improve map quality)

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Local search algorithm S* = {(P1, L02), (P2, L05), (P3, L12), (P4, L16), (P5, L18), (P6, L22) P1 List = {(L01, 1), (L02, 0)} S* = {(P1, L02), (P2, L05), (P3, L12), (P4, L16), (P5, L18), (P6, L22)} P2 List = {(L05, 0)} S* = {(P1, L02), (P2, L05), (P3, L12), (P4, L16), (P5, L18), (P6, L22)} P3 List = {(L09, 1), (L10, 2), (L11, 2), (L12,1)} S* = {(P1, L02), (P2, L05), (P3, L09), (P4, L16), (P5, L18), (P6, L22)}

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Results

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Standard sets of randomly generated points conditions described by Christensen et al. (1995) grid size of 792 by 612 units fixed size label of 30 by 7 units page size of 11 by 8.5 inch

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Test set Number of the points: N = 100, 250, 500, 750, 1000 Configurations: For each problem size, 25 different configurations with random placement of point features using different seeds; 4 label positions were considered for each point

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Percentage of labels without conflict for different number of points

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Computational times to reach the good solutions for different number of points (sec)

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After FALP application for 1000 random points (labels without overlap = 911)

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Conclusion The FALP showed quality results in label placement and excellent runtime performance We recommend to use FALP to solve point feature label placement for real time screen maps

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