On the Optimal Bisection of a Polygon
نویسندگان
چکیده
We show that bisecting a polygon into two equal (possibly disconnected) parts with the smallest possible total perimeter is NP-complete, and it is in fact NP-hard to approximate within any ratio. In contrast, we give a dynamic programming algorithm which nds a subdivision into two parts with total perimeter at most that of the optimum bisection, such that the two parts have areas within of each other; the time is polynomial in the number of sides of the polygon, and 1. When the polygon is convex, or if the parts are required to be connected, then the exact problem can be solved in quadratic time.
منابع مشابه
Matching of Polygon Objects by Optimizing Geometric Criteria
Despite the semantic criteria, geometric criteria have different performances on polygon feature matching in different vector datasets. By using these criteria for measuring the similarity of two polygons in all matchings, the same results would not have been obtained. To achieve the best matching results, the determination of optimal geometric criteria for each dataset is considered necessary....
متن کاملConnecting Yule Process, Bisection and Binary Search Tree via Martingales
We present new links between some remarkable martingales found in the study of the Binary Search Tree or of the bisection problem, looking at them on the probability space of a continuous time binary branching process.
متن کاملInstance Optimality of the Adaptive Maximum Strategy
In this paper, we prove that the standard adaptive finite element method with a (modified) maximum marking strategy is instance optimal for the total error, being the square root of the squared energy error plus the squared oscillation. This result will be derived in the model setting of Poisson’s equation on a polygon, linear finite elements, and conforming triangulations created by newest ver...
متن کاملTime-Invariant State Feedback Control Laws for a Special Form of Underactuated Nonlinear Systems Using Linear State Bisection
Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...
متن کاملLine Bisection Test Software to Evaluate the Visual-spatial Functions in Schizophrenic Patients
Introduction: One way to evaluate visual-spatial functions is to use line bisection test. With the advancement of information technology, this study attempted to design a line bisection test software and investigate its efficacy compared to the conventional paper-pencil form in schizophrenic patients. Method: The present study was a causal-comparative one and line bisection test software was de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- INFORMS Journal on Computing
دوره 4 شماره
صفحات -
تاریخ انتشار 1992