The number of intersections between two rectangular paths

Abstract

The authors consider upper bounds on the number of intersections between two rectangular paths. Let these two paths be denoted as P and Q, and denote the number of Manhattan subpaths in P and Q by mod P mod and mod Q mod respectively. K. Kant (1985) gave an upper bound of 10 mod P mod mod Q mod /9+4( mod P mod + mod Q mod )/9. The authors have sharpened these upper bounds, using methods to break the rectangular paths into subpaths, to be mod P mod mod Q mod +( mod P mod /2)+( mod Q mod /3), where they assume without loss of generality that mod P mod <or= mod Q mod .<<ETX>>