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Fast Coupled Path Planning: From Pseudo-Polynomial to Polynomial

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Computing and Combinatorics (COCOON 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

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Abstract

The coupled path planning (CPP) problem models the motion paths of the leaves of a multileaf collimator for optimally reproducing the prescribed dose in intensity-modulated radiation therapy (IMRT). Two versions of the CPP problem, unconstrained and constrained CPPs, are studied based on whether specifying the starting and ending positions of the leave paths. By exploring the underlying properties of the problem such as submodularity and L\(^\natural\)-convexity, we solve both CPP problems in polynomial time using the path-end hopping, local searching and proximity scaling techniques, improving current best known pseudo-polynomial time algorithms. Our algorithms are simple and easy to be implemented. Experimental results on real medical data showed that our CPP algorithms outperformed previous best-known algorithm by at least one order of magnitude.

This research was supported in part by the NSF grants CCF-0830402 and CCF-0844765, and the NIH grant K25-CA123112.

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References

  1. Ahuja, R., Hamacher, H.: A network flow algorithm to minimize beam-on time for unconstrained multileaf collimator problems in cancer radiation therapy. Networks 45(1), 36–41 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baatar, D., Hamacher, H., Ehrgott, M., Woeginger, G.: Decomposition of integer matrices and multileaf collimator sequencing. Discrete Applied Mathematics 152(1-3), 6–34 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bioucas-Dias, J., Valadão, G.: Phase unwrapping via graph cuts. IEEE Transactions on Image processing 16(3), 698 (2007)

    Article  MathSciNet  Google Scholar 

  4. Bortfeld, T., Kahler, D., Waldron, T., Boyer, A.: X-ray field compensation with multileaf collimators. International journal of radiation oncology, biology, physics 28(3), 723–730 (1994)

    Google Scholar 

  5. Chen, D.Z., Luan, S., Wang, C.: Coupled path planning, region optimization, and applications in intensity-modulated radiation therapy. In: Halperin, D., Mehlhorn, K. (eds.) Esa 2008. LNCS, vol. 5193, pp. 271–283. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Chen, D., Hu, X., Luan, S., Naqvi, S., Wang, C., Yu, C., Fleischer, R.: Generalized geometric approaches for leaf sequencing problems in radiation therapy. International Journal of Computational Geometry and Applications 16(2-3), 175–204 (2006)

    MATH  MathSciNet  Google Scholar 

  7. Converyt, D., Rosenbloom, M.: The generation of intensity-modulated fields for conformal I radiotherapy by dynamic collimation. Phys. Med. 37(6), 1359–1374 (1992)

    Article  Google Scholar 

  8. Fowler, J., Welsh, J., Howard, S.: Loss of biological effect in prolonged fraction delivery. International journal of radiation oncology, biology, physics 59(1), 242–249 (2004)

    Google Scholar 

  9. Hochbaum, D.S.: An efficient algorithm for image segmentation, markov random fields and related problems. J. ACM 48(4), 686–701 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hochbaum, D.: Complexity and algorithms for convex network optimization and other nonlinear problems. 4OR: A Quarterly Journal of Operations Research 3(3), 171–216 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kamath, S., Sahni, S., Palta, J., Ranka, S.: Algorithms for optimal sequencing of dynamic multileaf collimators. Physics in Medicine and Biology 49(1), 33–54 (2004)

    Article  Google Scholar 

  12. Kolmogorov, V., Shioura, A.: New Algorithms for the Dual of the Convex Cost Network Flow Problem with Application to Computer Vision. Mathematical Programming (2007) (submitted)

    Google Scholar 

  13. Murota, K.: Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10. In: Society for Industrial and Applied Mathematics, Philadelphia, PA,USA (2003)

    Google Scholar 

  14. Siochi, R.: Minimizing static intensity modulation delivery time using an intensity solid paradigm. International journal of radiation oncology, biology, physics 43(3), 671–680 (1999)

    Google Scholar 

  15. Spirou, S., Chui, C.: Generation of arbitrary intensity profiles by dynamic jaws or multileaf collimators. Medical Physics 21, 1031 (1994)

    Article  Google Scholar 

  16. Webb, S.: Intensity-modulated radiation therapy. Inst. of Physics Pub. Inc. (2001)

    Google Scholar 

  17. Yu, C.X., Luan, S., Wang, C., Chen, D.Z.: Single arc dose painting: An efficient method of precision radiation therapy. In: Provisional patent application. University of Maryland (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, the University of Iowa,  

    Yunlong Liu & Xiaodong Wu

  2. Department of Radiation Oncology, The University of Iowa,  

    Xiaodong Wu

Authors
  1. Yunlong Liu
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  2. Xiaodong Wu
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Editor information

Editors and Affiliations

  1. University of Florida, CSE Building, Room 566, P.O. Box 116120, 32611-6120, Gainesville, Florida, USA

    My T. Thai

  2. Department of Computer and Information Science and Technology, University of Florida, P.O. Box, USA

    Sartaj Sahni

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Liu, Y., Wu, X. (2010). Fast Coupled Path Planning: From Pseudo-Polynomial to Polynomial. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_45

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  • DOI: https://doi.org/10.1007/978-3-642-14031-0_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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