Lattice Embedding of Direction-Preserving Correspondence over Integrally Convex Set
consider the relationship of two fixed point theorems for direction-preserving discrete correspondences. We show that, for any space of no more than three dimensions, the fixed point theorem  of Iimura, Murota and Tamura, on integrally convex sets can be derived from Chen and Deng’s fixed point theorem  on lattices by extending every direction-preserving discrete correspondence over an integrally convex set to one over a lattice. We present a counter example for the four dimensional space. Related algorithmic results are also presented for finding a fixed point of direction-preserving correspondences on integrally convex sets, for spaces of all dimensions.
KeywordsTime Complexity Point Theorem Fixed Point Theorem Test Point Point Problem
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