Correction to "A Linear-Time Algorithm for Triangulating Simple Polygons"

نویسندگان

  • Robert E. Tarjan
  • Christopher J. Van Wyk
چکیده

The analysis showing that our triangulation algorithm runs in linear time is incorrect, and indeed the algorithm does not run in linear time in the worst case. So far we have been unable to obtain a linear-time algorithm for the triangulation problem. We have been able to obtain an 0 (n loglogn)-time algorithm, however. The details are described in ,cAn O(n loglogn)-Time Algorithm for Triangulating a Simple Polygon," SIAM Journal on Computing 17, 1 (February, 1988), to appear. [1] Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing (1986), 380-388.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Simple and Fast Incremental Randomized Algorithm for Computing Trapezoidal Decompositions and for Triangulating Polygons

Seidel, R., A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, Computational Geometry: Theory and Applications 1 (1991) 51-64. This paper presents a very simple incremental randomized algorithm for computing the trapezoidal decomposition induced by a set S of n line segments in the plane. If S is given as a simple polygona...

متن کامل

Triangulating and Guarding Realistic Polygons

We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards in the interior of the object. In this abstract, we describe a simple algorithm for triangulating k-guardable polygons. Our algorithm, which is easily implementable, takes linear time assuming that k is constant.

متن کامل

Triangulating a Simple Polygon in Linear Time

Triangulating a simple polygon has been one of the most outstanding open problems in two-dimensional computational geometry. It is a basic primitive in computer graphics and, generally, seems the natural preprocessing step for most nontrivial operations on simple polygons [5,13]. Recall that to triangulate a polygon is t o partition it into triangles without adding any new vertices. Despite its...

متن کامل

Fast Triangulation of the Plane with Respect to Simple Polygons

Let P~,..., Pk be pairwise non-intersecting simple polygons with a total of n vertices and s start vertices. A start vertex, in general, is a vertex both of which neighbors have larger x coordinate. We present an algorithm for triangulating P~,..., Pk in time O(n + s log s). s may be viewed as a measure of non-convexity. In particular, s is always bounded by the number of concave angles + 1, an...

متن کامل

Testing a Simple Polygon for Monotonicity Optimality in Parallel

Sumanta Guhat We show that, in parallel, an n-vertex simple polygon can be tested for monotonicity optimally in O(logn) time using O(n/logn) EREW PRAM processors, and we present two different optimal parallel algorithms for solving this problem. OUf result leads to an optimal parallcl algorithm for triangulating simple polygons that runs in O(logn) time using O(n/logn) EREW PRA!\I processors if...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1987