Tight Bounds for Visibility Matching of f-Equal Width Objects

Abstract

Abstract. Let s denote a compact convex object in IR 2 . The f-width of s is the perpendicular distance between two distinct parallel lines of support of s with direction f . A set of disjoint convex compact objects in IR 2 is of equal f -width if there exists a direction f such that every pair of objects have equal f -width. A visibility matching, for a set of equal f -width objects is a matching using non-crossing lines of site in the visibility graph of the set. In this note we establish tight bounds on the size of a maximal visibility matching for a set of f -equal width objects by showing that 2n 3 ≤ h(n) ≤ 2n 3 .

Matching Points with Things

“…The non-crossing requirement in our problems is quite natural in geometric scenarios (see for example [25,2,3]), and the family of geometric problems that we consider has several applications; these applications include geometric shape matching [4,13,17,18], colour-based image retrieval [13], music score matching [26], and computational biology [14,16].…”