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    • The Complexity of Comparing Optimal Solutions

    Da-Ren Chen,Min-Zheng Shieh,Shi-Chun Tsai

    Information Processing Letters（2022）

    Natl Yang Ming Chiao Tung Univ

    Cited 2|Views6
    Abstract
    delta(p) (2) is the complexity class of languages recognizable by deterministic Turing machines in polynomial time with an NP oracle. OptP is the class of functions computable by taking the maximum (or minimum) value of some function over a set of feasible solutions. In this work, we show that comparing the optimal values of two instances of some OptP- complete problems is delta(p)(2)-complete problem. We first prove that COMPWEIGHTEDMAXSAT is delta(p)(2)-complete and then generalize it to other OptP-complete problems, where COMPWEIGHTEDMAXSAT is the problem of comparing the optimal values of two instances of WEIGHTEDMAXSAT to determine whether the first optimal value is greater than the second one. (c) 2022 Elsevier B.V. All rights reserved.
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    Key words
    Computational complexity,Polynomial hierarchy,Delta(p)(2)-complete,WEIGHTEDMAXSAT,COMPWEIGHTEDMAXSAT
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