Lattice Embedding of Direction-Preserving Correspondence over Integrally Convex Set

(Extended Abstract)
  • Xi Chen
  • Xiaotie Deng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)


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.


Time Complexity Point Theorem Fixed Point Theorem Test Point Point Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xi Chen
    • 1
  • Xiaotie Deng
    • 2
  1. 1.Department of Computer ScienceTsinghua UniversityBeijingP.R. China
  2. 2.Department of Computer ScienceCity University of Hong KongHong Kong SAR

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