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Algorithms for Interval Structures with Applications

  • Danny Z. Chen
  • Ewa Misiołek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6681)

Abstract

We present new algorithms for two problems on interval structures that arise in computer-aided manufacturing and in other areas. We give an O(Kn) time algorithm for the single-source K-link shortest path problem on an interval graph with n weighted vertices, and two O(n) time algorithms for a generalized version of the optimal color-spanning problem for n points on a real line, where each point is assigned one of m colors (m ≤ n). A standard approach for solving the K-link shortest path problem would take O(Kn 2) time, and thus our result offers a linear time improvement. The previously best known algorithm for the optimal color-spanning problem in ℝ1 takes O(n) time and space. We provide two algorithms for a generalized version of this problem in which each color must appear a specified minimum number of times. One of these two solutions is suitable for an online processing of the (streaming) input points; it uses O(m) working space for the ordinary 1-D optimal color-spanning problem.

Keywords

Short Path Time Algorithm Interval Graph Left Endpoint Weighted Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Danny Z. Chen
    • 1
    • 2
  • Ewa Misiołek
    • 2
  1. 1.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.Mathematics DepartmentSaint Mary’s CollegeNotre DameUSA

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