Title: The Smallest Pair of Non-Crossing Paths in a Rectilinear Polygon
C. D. Yang
Avant! Corporation
46871 Bayside Parkway
Fremont, CA 94538
yangcd@avanticorp.com
D. T. Lee*
Department of Electrical and Computer Engineering
Northwestern University
Evanston, IL 60208 USA
dtlee@ece.nwu.edu
* Supported in part by the National Science Foundation under the
Grant CCR-9309743, and by the Office of Naval Research under
the Grants No. N00014-93-1-0272 and No. N00014-95-1-1007.
C. K. Wong
Department of Computer Science
Chinese University of Hong Kong
Shatin, New Territories, Hong Kong
wongck@cs.cuhk.hk
Abstract:
Smallest rectilinear paths are rectilinear paths with a minimum number
of bends and with a minimum length simultaneously. In this paper given
two pairs of terminals within a rectilinear polygon, we derive an
algorithm to find a pair of non-crossing rectilinear paths within
the polygon such that the total number of bends and the total length
are both minimized. Although a smallest rectilinear path between
two terminals in a rectilinear polygon always exists, we show that
such a smallest pair may not exist for some problem instances.
In that case the algorithm presented will either find among all
non-crossing paths with a minimum total number of bends, a pair
whose total length is the shortest, or find among all non-crossing
paths with a minimum total length, a pair whose total number of
bends is minimized. We provide a simple linear time and space
algorithm based on the fact that there are only a limited number of
configurations of such a solution pair.
IEEE Transactions on Computers, (46,8) August 1997, 930-941.