Lattice embedding of direction-preserving correspondence over integrally convex set

Authors:
Xi Chen;Xiaotie Deng
Affiliations:
Department of Computer Science, Tsinghua University, Beijing, P.R. China;Department of Computer Science, City University of Hong Kong, Hong Kong SAR
Venue:
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Year:
2006

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Abstract

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 [4] of Iimura, Murota and Tamura, on integrally convex sets can be derived from Chen and Deng's fixed point theorem [2] 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.