Staircase connected sets

Evelyn Magazanik*, Micha A. Perles

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

A compact set S ⊂ ℝR}2 is staircase connected if every two points a,b ∞ S can be connected by a polygonal path with sides parallel to the coordinate axes, which is both x-monotone and y-monotone. ξ(a,b) denotes the smallest number of edges of such a path. ξ(.,.) is an integer-valued metric on S. We investigate this metric and introduce stars and kernels. Our main result is that the r-th kernel is nonempty, compact and staircase connected provided r ≥ 1/2} · stdiam}(S)+1.

Original languageEnglish
Pages (from-to)587-599
Number of pages13
JournalDiscrete and Computational Geometry
Volume37
Issue number4
DOIs
StatePublished - May 2007

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