Long non-crossing configurations in the plane (Draft)

نویسندگان

  • Noga Alon
  • Subhash Suri
چکیده

It is shown that for any set of 2n points in general position in the plane there is a non-crossing perfect matching of n straight line segments whose total length is at least 2/π of the maximum possible total length of a (possibly crossing) perfect matching on these points. The constant 2/π is best possible and a non-crossing matching whose length is at least as above can be found in polynomial time. Similar results are obtained for the problem of finding a long non-crossing Hamilton path and a long non-crossing spanning tree for a given set of points in the plane.

برای دانلود رایگان 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

Generating functions and duality for non-crossing walks on a plane graph

The generating function for the number of non-crossing walk configurations of n walks between the roots of a two-rooted directed plane graph is introduced. This is shown to be a rational function and the structure and symmetry property of its numerator are discussed. The walk configurations correspond to flows and the equivalent dual generating function for potentials is investigated independen...

متن کامل

Random non-crossing plane configurations: A conditioned Galton-Watson tree approach

We study various models of random non-crossing configurations consisting of diagonals of convex polygons, and focus in particular on uniform dissections and non-crossing trees. For both these models, we prove convergence in distribution towards Aldous’ Brownian triangulation of the disk. In the case of dissections, we also refine the study of the maximal vertex degree and validate a conjecture ...

متن کامل

Analytic combinatorics of non-crossing configurations

This paper describes a systematic approach to the enumeration of 'non-crossing' geometric configurations built on vertices of a convex n-gon in the plane. It relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation. Consequences are both exact and asymptotic counting results for trees, forests, graphs, connected graphs, dissections, and partitions. Li...

متن کامل

Performance evaluation of modified bentlegPlow using finite element approach

ABSTRACT-This paper aims to develop a new design of a bentleg (BL) plow and to determine its performance as compared to the conventional one using finite element approach. The difference between the modified and conventional BL plows is the direction of angle between the projection of cutting blade on horizontal plane normal to plow shank and the line perpendicular to the plow shank in the same...

متن کامل

On Visibility Representations of Non-Planar Graphs

A rectangle visibility representation (RVR) of a graph consists of an assignment of axisaligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its endpoints. Testing whether a graph has an RVR is known to be NP-hard. In this paper, we study the problem of finding an RVR under the assumption that an embedding...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002