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Improving known solutions is hard

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Abstract

In this paper, we study the complexity of computing better solutions to optimization problems given other solutions. We use a model of computation suitable for this purpose, the counterexample computation model. We first prove that, if PH ≠ Σ 3P , polynomial time transducers cannot compute optimal solutions for many problems, even givenn 1−ε non-trivial solutions, for any ε>0. These results are then used to establish sharp lower bounds for several problems in the counterexample model. We extend the model by defining probabilistic counterexample computations and show that our results hold even in the presence of randomness.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, 14853, Ithaca, NY, USA

    Desh Ranjan, Suresh Chari & Pankaj Rohatgi

Authors
  1. Desh Ranjan
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  2. Suresh Chari
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  3. Pankaj Rohatgi
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Ranjan, D., Chari, S. & Rohatgi, P. Improving known solutions is hard. Comput Complexity 3, 168–185 (1993). https://doi.org/10.1007/BF01200119

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