Matching Points with Rectangles and Squares

نویسندگان

  • Sergey Bereg
  • Nikolaus Mutsanas
  • Alexander Wolff
چکیده

In this paper we deal with the following natural family of geometric matching problems. Given a class C of geometric objects and a point set P , a C-matching is a set M ⊆ C such that every C ∈ M contains exactly two elements of P . The matching is perfect if it covers every point, and strong if the objects do not intersect. We concentrate on matching points using axis-aligned squares and rectangles. We give algorithms for these classes and show that it is NP-hard to decide whether a point set has a perfect strong square matching. We show that one of our matching algorithms solves a family of map-labeling problems.

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

Matching colored points with rectangles

Let S be a point set in the plane such that each of its ele1 ments is colored either red or blue. A matching of S with rectangles is 2 any set of pairwise-disjoint axis-aligned rectangles such that each rectan3 gle contains exactly two points of S. Such a matching is monochromatic 4 if every rectangle contains points of the same color, and is bichromatic if 5 every rectangle contains points of ...

متن کامل

Two Dimensional Matching 10.1 Exact Matching

String matching is a basic theoretical problem in computer science, but has been useful in implementating various text editing tasks. The explosion of multimedia requires an appropriate generalization of string matching to higher dimensions. The rst natural generalization is that of seeking the occurrences of a pattern in a text where both pattern and text are rectangles. The last few years saw...

متن کامل

Finding Squares and Rectangles in Sets of Points

The following problem is studied: Given a set S of n points in the plane, does it contain a subset of four points that form the vertices of a square or rectangle. Both the axis-parallel case and the arbitrarily oriented case are studied. We also investigate extensions to the d-dimensional case. Algorithms are obtained that run in O( n1+1/ d log n) time for axis-parallel squares and O( n21/ d ) ...

متن کامل

On the Optimality of an Algorithm of Reingold and Supowit

Let n be an even integer, and P a set of n points in the plane. A matching is a set of n/2 edges such that each point of P is an endpoint of exactly one edge. The sum of the lengths of the edges is called the cost of the matching. In [], Reingold and Supowit have analyzed a divide–and–conquer heuristic to obtain a matching with a small cost. Here, we want to demonstrate, that – among a large cl...

متن کامل

Matching Rectangles in d - Dimensions : Algorithms and Laws of Large Numbers

For each point of the integer lattice Zd, let X and Y be independent identically distributed random variables with P(X = Y) = p E (0, 1). Let S(n) be the volume of the largest d-dimensional cube in ( I , ..., n t d with the property that X = Y at every point of the cube; R ( n ) is similarly defined to be the maximum volume of perfectly matching rectangles. It is proved that, if all possible sh...

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 2006