Stabbing pairwise intersecting disks by five points

نویسندگان

  • Sariel Har-Peled
  • Haim Kaplan
  • Wolfgang Mulzer
  • Liam Roditty
  • Paul Seiferth
  • Micha Sharir
  • Max Willert
چکیده

We present a deterministic linear time algorithm to find a set of five points that stab a set of n pairwise intersecting disks in the plane. We also give a simple construction with 13 pairwise intersecting disks that cannot be stabbed by three points.

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

Efficient constant factor approximation algorithms for stabbing line segments with equal disks

Fast constant factor approximation algorithms are devised for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0, where the set of segments forms a straight line drawing G = (V,E) of a planar graph without edge crossings. Exploiting its tough connection with the geometric Hitting Set problem we give (

متن کامل

Fast Stabbing of Boxes in High Dimensions

We present in this paper a simple yet e cient algorithm for stabbing a set S of n axisparallel boxes in d-dimensional space with c(S) points in output-sensitive time O(dn log c(S)) and linear space. Let c∗(S) and b∗(S) be, respectively, the minimum number of points required to stab S and the maximum number of pairwise disjoint boxes of S. We prove that b(S)6c(S)6c(S)6b(S)(1+log2 b ∗(S))d−1. Sin...

متن کامل

New Results on Stabbing Segments with a Polygon

We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or pe...

متن کامل

Convex Transversals

We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem re...

متن کامل

The Maximum Indpendent Set Problem in Unit Disk Graphs

The class of intersection graphs of disks in the Euclidean plane, called disk graphs, was studied for many years for its theoretical aspects as well as for its applications. The maximum independent set problem on disk graphs (computing a largest subset of the given disks such that the disks in the subset are pairwise disjoint) has applications in map labeling. Under the assumption that labels o...

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:
  • CoRR

دوره abs/1801.03158  شماره 

صفحات  -

تاریخ انتشار 2018