On the Complexity of Finding Paths in a Two-Dimensional Domain II: Piecewise Straight-Line Paths

Abstract

The problem of finding a piecewise straight-line path, with a constant number of line segments, in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. It is proved that, for polynomial-time recognizable domains associated with polynomial-time computable distance functions, the complexity of this problem is equivalent to a discrete problem which is complete for ∑2P, the second level of the polynomial-time hierarchy.