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Reconstructing Numbers from Pairwise Function Values

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

The turnpike problem is one of the few “natural” problems that are neither known to be NP-complete nor solvable by efficient algorithms. We seek to study this problem in a more general setting. We consider the generalized problem which tries to resolve set A = {a 1,a 2, ⋯ ,a n } from pairwise function values {f(a i ,a j ) | 1 ≤ i, j ≤ n} for a given bivariate function f. We call this problem the Number Reconstruction problem. Our results include efficient algorithms when f is monotone and non-trivial bounds on the number of solutions when f is the sum. We also generalize previous backtracking and algebraic algorithms for the turnpike problem such that they work for the family of anti-monotone functions and linear-decomposable functions. Finally, we propose an efficient algorithm for the string reconstruction problem, which is related to an approach to protein reconstruction.

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Author information

Authors and Affiliations

  1. Tsinghua University, Beijing, 100084, China

    Shiteng Chen

  2. University of Pennsylvania, Philadelphia, PA 19104, USA

    Zhiyi Huang & Sampath Kannan

Authors
  1. Shiteng Chen
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  2. Zhiyi Huang
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  3. Sampath Kannan
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Chen, S., Huang, Z., Kannan, S. (2009). Reconstructing Numbers from Pairwise Function Values. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_16

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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