Largest area convex hull of imprecise data based on axis-aligned squares

Authors:
Wenqi Ju;Jun Luo;Binhai Zhu;Ovidiu Daescu
Affiliations:
Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China and Graduate University of the Chinese Academy of Sciences, Beijing, China and Shenzhen Institutes of Advanced Techno ...;Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China;Department of Computer Science, Montana State University, Bozeman, USA;Department of Computer Science, University of Texas at Dallas, Dallas, USA
Venue:
Journal of Combinatorial Optimization
Year:
2013

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Abstract

In recent years, more and more algorithms related to imprecise data have been proposed. Specifically, some algorithms on computing the maximum area convex hull are designed recently when the imprecise data are modeled as non-overlapping axis-aligned squares or as equal size squares. The time complexity of the best known algorithm based on non-overlapping axis-aligned squares is O(n7). If the squares have equal size and can overlap, the time complexity of the best known algorithm is O(n5). In this paper, we improve the former from O(n7) to O(n5) and improve the latter from O(n5) to O(n2). These results are obtained by exploiting the non-trivial geometric properties of the problems.