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Maximum Red/Blue Interval Matching with Application

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Computing and Combinatorics (COCOON 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2108))

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Abstract

In this paper, we consider the problem of computing a maximum cardinality matching among a set I of n intervals that are colored as either red or blue, such that a pair of intervals in I can be matched only if they overlap with each other and have different colors. This problem arises in some applications such as radiosurgery treatment planning. We present a greedy algorithm for this problem that runs in O(n log log n) time for sorted input.We also solve a useful generalization of this red/blue interval matching problem in the same time bound.

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References

  1. M.G. Andrews, M.J. Atallah, D.Z. Chen, and D.T. Lee, “Parallel algorithms for maximum matching in complements of interval graphs and related problems,” Algorithmica, 26(2) (2000), pp. 263–289.

    Article  MATH  MathSciNet  Google Scholar 

  2. M.G. Andrews and D.T. Lee, “An optimal algorithm for matching in interval graphs,” manuscript, 1992.

    Google Scholar 

  3. D.Z. Chen, X. Wu, L. Zhang, X. Hu, and C. Yu, “A new algorithm for intensitymodulated arc therapy (IMAT) with dynamic multileaf collimation,” manuscript, 2001.

    Google Scholar 

  4. T.H. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms, McGraw-Hill, New York, NY, 1990.

    Google Scholar 

  5. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.

    MATH  Google Scholar 

  6. J.E. Hopcroft and R.M. Karp, “An n5/2 algorithm for maximum matchings in bipartite graphs,” SIAM J. Comput., 2 (1973), pp. 225–231.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Moitra and R.C. Johnson, “A parallel algorithm for maximum matching in interval graphs,” Proc. Int. Conf. Parallel Processing, 1989, Vol. III, pp. 114–120.

    Google Scholar 

  8. F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.

    Google Scholar 

  9. P. van Emde Boas, “Preserving order in a forest in less than logarithmic time and linear space,” Information Processing Letters, 6(3) (1977), pp. 80–82.

    Article  MATH  Google Scholar 

  10. P. van Emde Boas, R. Kaas, and E. Zijlstra, “Design and implementation of an efficient priority queue,” Mathematical Systems Theory, 10 (1977), pp. 99–127.

    Article  MATH  Google Scholar 

  11. C.X. Yu, personal communication, January 2001.

    Google Scholar 

  12. C.X. Yu, D. Yan, M.N. Du, S. Zhou, and L.J. Verhey, “Optimization of leaf positioning when shaping a radiation field with a multileaf collimator,#x201D; Phys. Med. Biol., 40(2) (1995), pp. 305–308.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Danny Z. Chen & Xiaobo Sharon Hu

Authors
  1. Danny Z. Chen
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  2. Xiaobo Sharon Hu
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  3. Xiaodong Wu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts, One University Avenue, Lowell, MA, 01854, USA

    Jie Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Chen, D.Z., Hu, X.S., Wu, X. (2001). Maximum Red/Blue Interval Matching with Application. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_17

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  • DOI: https://doi.org/10.1007/3-540-44679-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42494-9

  • Online ISBN: 978-3-540-44679-8

  • eBook Packages: Springer Book Archive

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