• Corpus ID: 772478

Spanning Colored Points with Intervals

@inproceedings{Khanteimouri2013SpanningCP,
  title={Spanning Colored Points with Intervals},
  author={Payam Khanteimouri and Ali Mohades and Mohammad Ali Abam and Mohammad Reza Kazemi},
  booktitle={CCCG},
  year={2013}
}
We study a variant of the problem of spanning colored objects where the goal is to span colored objects with two similar regions. We dedicate our attention in this paper to the case where objects are points lying on the real line and regions are intervals. Precisely, the goal is to compute two intervals together spanning all colors. As the main ingredient of our algorithm, we first introduce a kinetic data structure to keep track of minimal intervals spanning all colors. Then we present a novel… 

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References

SHOWING 1-10 OF 13 REFERENCES

Smallest Color-Spanning Object Revisited

A dynamic version of the problem is studied, where new points may be added, and the narrowest color-spanning corridor at any instance can be reported in O(mn(α(n))2log m) time.

On some geometric problems of color-spanning sets

This paper proposes an O(n1+ε) time algorithm for the maximum diameter color-spanning set problem where ε could be an arbitrarily small positive constant and proposes two efficient constant factor approximation algorithms for the planar smallest perimeter color- spanning convex hull problem.

Algorithms for interval structures with applications

The Farthest Color Voronoi Diagram and Related Problems

This paper provides algorithms that may help to achieve this goal for various specifications of the term “neighborhood” for various types of facilities modeled by n colored points in the plane, each type by its own color.

The upper envelope of voronoi surfaces and its applications

Borders on the number of vertices on the upper envelope of a collection of Voronoi surfaces are derived, and efficient algorithms to calculate these vertices are provided.

On Enclosing k Points by a Circle

  • J. Matoušek
  • Computer Science, Mathematics
    Inf. Process. Lett.
  • 1995

Further Results on Generalized Intersection Searching Problems: Counting, Reporting, and Dynamization

A uniform framework is presented to solve efficiently the counting/reporting/dynamic versions of a variety of generalized intersection searching problems, including: 1-, 2-, and 3-dimensional range searching, quadrant searching, and 2-dimensional point enclosure searching.

Finding k points with a smallest enclosing square

  • M. Smid
  • Computer Science, Mathematics
  • 1993
An algorithm is presented that, given a set of n points in the plane and an integer k, 2 ≤ k ≤ n, finds k points with a smallest enclosing axes-parallel square. The algorithm has a running time of

Kinetic Data Structures

  • L. Guibas
  • Computer Science
    Handbook of Data Structures and Applications
  • 2004
A new type of data structure is created, called a kinetic data structure, made of a proof of correctness of the attribute which is animated through time by a discrete event simulation.

Smallest Color-Spanning Objects

This paper shows for a set of colored point sites in the plane how to compute the smallest-- by perimeter or area--axis-parallel rectangle and the narrowest strip enclosing at least one site of each color.