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<p>We review recent methodological developments of algorithm engineering and computational geometry from the perspective of geoinformation science and cartography. To exemplify these developments, we discuss research on tasks of map generalization, urban analytics, regionalization, trajectory analysis, and surface modeling that require efficient processing of geometric objects and, in particular, their simplification, clustering, and aggregation. Algorithm engineering provides a&#xa0;systematic approach to developing practical algorithms with proven guarantees, using a&#xa0;formal model of the real-world problem of interest as a&#xa0;starting point. Since in geoinformation science and cartography modeling a&#xa0;problem can be a&#xa0;major research challenge, we emphasize the importance of incorporating a&#xa0;feedback loop for incremental problem modeling in the algorithm engineering approach. Moreover, we highlight the relevance of graph-theoretic concepts and algorithms as well as distances measuring the dissimilarity of geometric objects and graphs, to model problems in a&#xa0;form that is accessible for algorithms. As concrete algorithmic techniques we review graph cuts, spectral clustering, graph similarity measures, graph embedding techniques, clustering methods for trajectories, optimization by integer programming, and data-dependent as well as higher-order Delaunay triangulations.</p>

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Geoinformation Perspectives on Recent Developments in Algorithm Engineering and Computational Geometry

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月6日

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  • Jan-Henrik Haunert,
  • Anne Driemel,
  • Petra Mutzel

摘要

We review recent methodological developments of algorithm engineering and computational geometry from the perspective of geoinformation science and cartography. To exemplify these developments, we discuss research on tasks of map generalization, urban analytics, regionalization, trajectory analysis, and surface modeling that require efficient processing of geometric objects and, in particular, their simplification, clustering, and aggregation. Algorithm engineering provides a systematic approach to developing practical algorithms with proven guarantees, using a formal model of the real-world problem of interest as a starting point. Since in geoinformation science and cartography modeling a problem can be a major research challenge, we emphasize the importance of incorporating a feedback loop for incremental problem modeling in the algorithm engineering approach. Moreover, we highlight the relevance of graph-theoretic concepts and algorithms as well as distances measuring the dissimilarity of geometric objects and graphs, to model problems in a form that is accessible for algorithms. As concrete algorithmic techniques we review graph cuts, spectral clustering, graph similarity measures, graph embedding techniques, clustering methods for trajectories, optimization by integer programming, and data-dependent as well as higher-order Delaunay triangulations.