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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 The combinatorial explosion of possible solutions**

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**

• 1 point 2¹ configurations P1/L0 P1/L1 2 points 2² configurations P2/L0 P2/L1 P2/L0 P2/L1 3 points 2³ configurations P3/L0 P3/L1 P3/L0 P3/L1 • • • • • • • • • • • • • • 1000 points 2¹ººº configurations • • • •

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**Two points – potential label positions and corresponding conflict graph**

Candidate label positions Conflict 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)} 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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