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Shortest path length with bounded-alternation \((\min ,+)\) formulas

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Abstract

We study bounded-depth \((\min ,+)\) formulas computing the shortest path polynomial. For depth 2d with \(d \ge 2\), we obtain lower bounds parameterized by certain fan-in restrictions on \(+\) gates except those at the bottom level. For depth 4, in two regimes of the parameter, the bounds are tight.

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References

  1. Jukna, S.: Limitations of incremental dynamic programming. Algorithmica 69(2), 461–492 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Jukna, S.: Lower bounds for tropical circuits and dynamic programs. Theory Comput. Syst. 57(1), 160–194 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jukna, S.: Tropical complexity, Sidon sets, and dynamic programming. SIAM J. Discrete Math. 30(4), 2064–2085 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jukna, S.: Incremental versus non-incremental dynamic programming. Electron. Colloq. Comput. Complex. (ECCC) 25, 42 (2018)

    Google Scholar 

  5. Bellman, R.: On a routing problem. Q. Appl. Math. 16, 87–90 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ford Jr, L.R.: Network flow theory. Technical Report P-923, Rand Corporation (1956)

  7. Jukna, S., Schnitger, G.: On the optimality of bellman-ford-moore shortest path algorithm. Theor. Comput. Sci. 628, 101–109 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  8. Karchmer, M., Wigderson, A.: Monotone circuits for connectivity require super-logarithmic depth. SIAM J. Discrete Math. 3(2), 255–265 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  9. Håstad, J.: Computational Limitations of Small-Depth Circuits. MIT Press, Cambridge (1987)

    Google Scholar 

  10. Chen, X., Oliveira, I.C., Servedio, R.A., Tan, L.Y.: Near-optimal small-depth lower bounds for small distance connectivity. In: Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing, STOC ’16, pp. 612–625 (2016)

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, HBNI, Chennai, 600113, India

    Meena Mahajan & Anuj Tawari

  2. Chennai Mathematical Institute, Chennai, India

    Prajakta Nimbhorkar

Authors
  1. Meena Mahajan
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  2. Prajakta Nimbhorkar
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  3. Anuj Tawari
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Correspondence to Meena Mahajan.

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Mahajan, M., Nimbhorkar, P. & Tawari, A. Shortest path length with bounded-alternation \((\min ,+)\) formulas. Int J Adv Eng Sci Appl Math 11, 68–74 (2019). https://doi.org/10.1007/s12572-018-0229-6

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  • DOI: https://doi.org/10.1007/s12572-018-0229-6

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