TY - JOUR
T1 - Staircase connected sets
AU - Magazanik, Evelyn
AU - Perles, Micha A.
PY - 2007/5
Y1 - 2007/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=34247599881&partnerID=8YFLogxK
U2 - 10.1007/s00454-007-1308-9
DO - 10.1007/s00454-007-1308-9
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AN - SCOPUS:34247599881
SN - 0179-5376
VL - 37
SP - 587
EP - 599
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 4
ER -