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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.<\/jats:p>\n          <jats:p>\n            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\n            <jats:sup>\u22c6<\/jats:sup>\n            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\n            <jats:sup>\u22c6<\/jats:sup>\n            finds optimal aggregation sequences for more instances than the other two methods within a given time frame.\n          <\/jats:p>","DOI":"10.1145\/3409290","type":"journal-article","created":{"date-parts":[[2020,10,14]],"date-time":"2020-10-14T11:32:54Z","timestamp":1602675174000},"page":"1-40","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Finding Optimal Sequences for Area Aggregation\u2014A\n            <sup>\u22c6<\/sup>\n            vs. Integer Linear Programming"],"prefix":"10.1145","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6848-3545","authenticated-orcid":false,"given":"Dongliang","family":"Peng","sequence":"first","affiliation":[{"name":"Section GIS Technology, Delft University of Technology, The Netherlands and Chair of Computer Science I, University of W\u00fcrzburg, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5872-718X","authenticated-orcid":false,"given":"Alexander","family":"Wolff","sequence":"additional","affiliation":[{"name":"Chair of Computer Science I, University of W\u00fcrzburg, Am Hubland, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8005-943X","authenticated-orcid":false,"given":"Jan-Henrik","family":"Haunert","sequence":"additional","affiliation":[{"name":"Institute of Geodesy and Geoinformation, University of Bonn, Germany"}]}],"member":"320","published-online":{"date-parts":[[2020,10,14]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Arbeitsgemeinschaft der Vermessungsverwaltungender L\u00e4nder der Bundesrepublik Deutschland (AdV). 2003. 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Addison-Wesley Publishing Company. Retrieved from http:\/\/web.mit.edu\/15.053\/www\/AMP.htm."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1559\/152304007780279078"},{"key":"e_1_2_1_4_1","volume-title":"Controlled line smoothing by snakes. GeoInformatica 9, 3 (01","author":"Burghardt Dirk","year":"2005","unstructured":"Dirk Burghardt . 2005. Controlled line smoothing by snakes. GeoInformatica 9, 3 (01 Sept. 2005 ), 237--252. DOI:https:\/\/doi.org\/10\/dfjwz5 Dirk Burghardt. 2005. Controlled line smoothing by snakes. GeoInformatica 9, 3 (01 Sept. 2005), 237--252. 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