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Handbook of Combinatorial Optimization pp 41–92Cite as

Advanced Techniques for Dynamic Programming

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Abstract

This is an overview over dynamic programming with an emphasis on advanced methods. Problems discussed include path problems, construction of search trees, scheduling problems, applications of dynamic programming for sorting problems, server problems, as well as others. This chapter contains an extensive discussion of dynamic programming speedup. There exist several general techniques in the literature for speeding up naive implementations of dynamic programming. Two of the best known are the Knuth-Yao quadrangle inequality speedup and the SMAWK/LARSCH algorithm for finding the row minima of totally monotone matrices. The chapter includes “ready to implement” descriptions of the SMAWK and LARSCH algorithms. Another focus is on dynamic programming, online algorithms, and work functions.

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Notes

  1. 1.

    Use the leftmost rule to break ties.

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Acknowledgements

This chapter is dedicated to Lawrence L. Larmore, a great mentor. A sabbatical (academic year 2006/07) granted by the University of Nevada, Las Vegas, which benefited this book chapter, is acknowledged.

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  1. University of Nevada, Las Vegas, Department of Computer Science, 4505 Maryland Parkway, 89154-4019, Las Vegas, NV, USA

    Wolfgang Bein

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  1. Wolfgang Bein
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Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Bein, W. (2013). Advanced Techniques for Dynamic Programming. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_28

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