Monotone path systems in simple regions

Abstract

A monotone path system (MPS) is a finite set of pairwise disjoint paths (polygonal areas) in thexy-plane such that every horizontal line intersects each of the paths in at most one point. A MPS naturally determines a “pairing” of its top points with its bottom points. We consider a simple polygon Δ in thexy-plane wich bounds the simple polygonal (closed) regionD. LetT andB be two finite, disjoint, equicardinal sets of points ofD. We give a good characterization for the existence of a MPS inD which pairsT withB, and a good algorithm for finding such a MPS, and we solve the problem of finding all MPSs inD which pairT withB. We also give sufficient conditions for any such pairing to be the same.

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The first author's research is supported by the Natural Sciences and Engineering Research Council of Canada

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Cameron, K., Sachs, H. Monotone path systems in simple regions. Combinatorica 14, 1–21 (1994). https://doi.org/10.1007/BF01305947

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AMS subject classification codes (1980)

  • 52 A 37
  • 05 C 38
  • 05 C 70