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.
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Chen, D.Z., Misiołek, E. (2011). Algorithms for Interval Structures with Applications. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_23
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DOI: https://doi.org/10.1007/978-3-642-21204-8_23
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