The ultimate planar convex hull algorithm
SIAM Journal on Computing
Splitsort—an adaptive sorting algorithm
Information Processing Letters
A survey of adaptive sorting algorithms
ACM Computing Surveys (CSUR)
Journal of Algorithms
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Adaptive set intersections, unions, and differences
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Multidimensional binary search trees used for associative searching
Communications of the ACM
Adaptive intersection and t-threshold problems
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
ICCI '91 Proceedings of the International Conference on Computing and Information: Advances in Computing and Information
Adaptive Algorithms for Constructing Convex Hulls and Triangulations of Polygonal Chains
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Priority Queues, Pairing, and Adaptive Sorting
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A new representation for linear lists
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
Space-efficient geometric divide-and-conquer algorithms
Computational Geometry: Theory and Applications
Adaptive searching in succinctly encoded binary relations and tree-structured documents
Theoretical Computer Science
Adaptive sorting: an information theoretic perspective
Acta Informatica
Journal of Computer and System Sciences
Cache-aware and cache-oblivious adaptive sorting
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We study problems in computational geometry from the viewpoint of adaptive algorithms. Adaptive algorithms have been extensively studied for the sorting problem, and in this paper we generalize the framework to geometric problems. To this end, we think of geometric problems as permutation (or rearrangement) problems of arrays, and define the "presortedness" as a distance from the input array to the desired output array. We call an algorithm adaptive if it runs faster when a given input array is closer to the desired output, and furthermore it does not make use of any information of the presortedness. As a case study, we look into the planar convex hull problem for which we discover two natural formulations as permutation problems. An interesting phenomenon that we prove is that for one formulation the problem can be solved adaptively, but for the other formulation no adaptive algorithm can be better than an optimal output-sensitive algorithm for the planar convex hull problem.