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1995•SIAM Journal on ComputingRequires access

Computational Complexity of Two-Dimensional Regions

Arthur W. Chou, Ker‐I Ko

Open publisher page 43 citations

Abstract

The computational complexity of bounded sets of the two-dimensional plane is studied in the discrete computational model. We introduce four notions of polynomial-time computable sets in ${\bf R}^{2}$ and study their relationship. The computational complexity of the winding number problem, membership problem, distance problem, and area problem is characterized by the relations between discrete complexity classes of the NP theory.

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What this paper is about

The computational complexity of bounded sets of the two-dimensional plane is studied in the discrete computational model. We introduce four notions of polynomial-time computable sets in ${\bf R}^{2}$ and study their relationship. The computational complexity of the winding number problem, membership problem, distance problem, and area problem is characterized by the relations between discrete complexity classes of the NP theory.

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Available abstract

The computational complexity of bounded sets of the two-dimensional plane is studied in the discrete computational model. We introduce four notions of polynomial-time computable sets in ${\bf R}^{2}$ and study their relationship. The computational complexity of the winding number problem, membership problem, distance problem, and area problem is characterized by the relations between discrete complexity classes of the NP theory.

Key concepts: Structural complexity theory, Computational complexity theory, Computational resource, PH, Asymptotic computational complexity, Quantum complexity theory, Complexity class, Mathematics

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