Solving Related Two-and Three-Dimensional Linear Programming Problems in Logarithmic Time

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Leonidas J. Guibas, Jorge Stolfi, Kenneth L. Clarkson

Published: 1987, Last Modified: 12 May 2025Theor. Comput. Sci. 1987EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Given n linear inequalities in three variables, we show how to construct a corresponding spherical subdivision using great circle arcs in time O(n log n) and space O(n). This subdivision in turn allows us to compute the point in space satisfying all inequalities and maximizing any desired linear objective function in time O(log n).