The site perimeter enumeration of polyominoes that are both columnand row-convex is a well-understood problem that always yields algebraic generating functions. Counting more general families of polyominoes is a far more difficult problem. Here Mireille BousquetMélou and Andrew Rechnitzer enumerate (by their site perimeter) the simplest family of polyominoes that are not fully convex—bargraphs....

We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For Ω ⊂ D = (0, 1), with d ≥ 2, we are given n random i.i.d. points on D whose membership in Ω is known. We consider the sample as a random geometric graph with connection distance ε > 0. We estimate the perimeter of Ω (relative to D) by the, appropriately rescaled, graph cut between the vertices...

Global placement of hypergraphs is critical in the top-down placement of large timing-driven designs 10, 16]. Placement quality is evaluated in terms of the half-perimeter wirelength (HPWL) of hyperedges in the original circuit hypergraph provided timing constraints are met. Analytical placers are instrumental in handling non-linear timing models 9, 3], but have two important drawbacks: (a) cor...

Introduction Let P = p1, . . . , pn be a simple polygon (all polygons are assumed convex throughout this paper). A fundamental problem in geometric optimization is to compute a minimum-area or a minimum-perimeter convex k-gon (denoted QA or Qp, resp.) that encloses P . While efficient algorithms for finding QA are known for more than 20 years [8, 1, 2], the problem of finding Qp has remained op...

Uncontrolled variables often limit meaningful assessment of visual sensitivity. Previously, we developed a procedure and apparatus for in vivo assessment of light absorption by the human lens. In the current study, we modified a widely used automated perimeter to include our procedure for obtaining an index of lens density. Nineteen individuals were tested on both the original apparatus and the...

We consider generalizations of the honeycomb problem to the sphere S and seek the perimeter-minimizing partition into n regions of equal area. We provide a new proof of Masters’ result that three great semicircles meeting at the poles at 120 degrees minimize perimeter among partitions into three equal areas. We also treat the case of four equal areas, and we prove under various hypotheses that ...

Given a set of points P in the plane and profits (or prizes) π : P → R≥0 we want to select a maximum profit set X ⊆ P which maximizes P p∈X π(p) − μ(X) for some particular criterion μ(X). In this paper we consider four such criteria, namely the perimeter and the area of the smallest axis-parallel rectangle containing X, and the perimeter and the area of the convex hull conv(X) of X. Our key res...