A green transportation system composed of transit, busses and bicycles could be a significant in alleviating traffic congestion. However, the inaccuracy of current transit ridership forecasting methods is imposing a negative impact on the development of urban transit systems. Traffic Analysis Zone (TAZ) delineating is a fundamental and essential step in ridership forecasting, existing delineati...

The problem considered in this article is: ‘for given finite system of convex polygons in the plane which have no transversal, find such homothety transformations of polygons (having fixed centres inside given polygons) with minimal similarity ratio c > 1 that the transformed system has a transversal’. We prove that in this ‘minimal configuration’, we can always find three polygons (two of them...

We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a connection between the reciprocity results known to combinatorialists and the inversion relations used by physicists to solve models in statistical mechanics. Fo...

A set of polygons is called c-oriented if the edges of all polygons are oriented in a constant number of previously defined directions. The intersection searching problem is studied for such objects, namely: Given a set of c-oriented polygons P and a c-oriented query polygon q, find all polygons in P that intersect q. It is shown that this problem can be solved in O(logZn + t) time with O(n log...

We study the class of rectilinear polygons, called X Y polygons, with horizontal and vertical edges, which are frequently used as building blocks for very large-scale integrated (VLSI) circuit layout and wiring. In the paper we introduce the notion of convexity within the.~class of X Y polygons and present efficient algorithms for computing the X Y convex hulls of an X Y polygon and of a set of...

We study the topology of moduli spaces of polygons with xed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with xed side lengths and marked convex Euclidean polygons with prescribed angles. 1. We consider the space P n of all polygons with n distinguished vertices in the Euclidean plane E 2 whose sides have nonnegative length allowing...

We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp[pA− Jb] to a polygon with area A and b bends. For convex and column-convex polygons, we show that 〈A〉/Amax = 1−K(J)/p̃ 2 + O(ρ), where p̃ = pN ≫ 1, and ρ < 1. The constant K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons sh...

Low efficiency of interference calculation has become the bottleneck that restricts further development of the performance of evolutionary algorithm for the polygon layout. To solve the problem, in this paper, we propose an algorithm of calculating overlapping area between two irregular polygons. For this algorithm, at first, two irregular polygons are respectively decomposed into the minimum n...