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Finding Optimal Sequences for Area Aggregation—A^⋆ vs. Integer Linear Programming

Authors:

Dongliang Peng,

Alexander Wolff,

Jan-Henrik HaunertAuthors Info & Claims

ACM Transactions on Spatial Algorithms and Systems (TSAS), Volume 7, Issue 1

Article No.: 4, Pages 1 - 40

https://doi.org/10.1145/3409290

Published: 14 October 2020 Publication History

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Abstract

To provide users with maps of different scales and to allow them to zoom in and out without losing context, automatic methods for map generalization are needed. We approach this problem for land-cover maps. Given two land-cover maps at two different scales, we want to find a sequence of small incremental changes that gradually transforms one map into the other. We assume that the two input maps consist of polygons, each of which belongs to a given land-cover type. Every polygon on the smaller-scale map is the union of a set of adjacent polygons on the larger-scale map.

In each step of the computed sequence, the smallest area is merged with one of its neighbors. We do not select that neighbor according to a prescribed rule but compute the whole sequence of pairwise merges at once, based on global optimization. We have proved that this problem is NP-hard. We formalize this optimization problem as that of finding a shortest path in a (very large) graph. We present the A^⋆ algorithm and integer linear programming to solve this optimization problem. To avoid long computing times, we allow the two methods to return non-optimal results. In addition, we present a greedy algorithm as a benchmark. We tested the three methods with a dataset of the official German topographic database ATKIS. Our main result is that A^⋆ finds optimal aggregation sequences for more instances than the other two methods within a given time frame.

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Cited By

Peng DMeijers Mvan Oosterom P(2023)Generalizing Simultaneously to Support Smooth Zooming: Case Study of Merging Area ObjectsJournal of Geovisualization and Spatial Analysis10.1007/s41651-022-00109-x7:1Online publication date: 11-May-2023
https://doi.org/10.1007/s41651-022-00109-x

Index Terms

Finding Optimal Sequences for Area Aggregation—A^⋆ vs. Integer Linear Programming
1. Applied computing
  1. Computers in other domains
    1. Cartography

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cover image ACM Transactions on Spatial Algorithms and Systems

ACM Transactions on Spatial Algorithms and Systems Volume 7, Issue 1

March 2021

161 pages

ISSN:2374-0353

EISSN:2374-0361

DOI:10.1145/3417500

Editor:
Walid G. Aref
Purdue University, USA

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© 2020 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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Publication History

Published: 14 October 2020

Accepted: 01 June 2020

Revised: 01 June 2020

Received: 01 April 2019

Published in TSAS Volume 7, Issue 1

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Peng DMeijers Mvan Oosterom P(2023)Generalizing Simultaneously to Support Smooth Zooming: Case Study of Merging Area ObjectsJournal of Geovisualization and Spatial Analysis10.1007/s41651-022-00109-x7:1Online publication date: 11-May-2023
https://doi.org/10.1007/s41651-022-00109-x

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