关于近似最优加权游说和正确率与平均情况多项式时间的关系
On Approximating Optimal Weighted Lobbying, and Frequency of Correctness versus Average-Case Polynomial Time
摘要：
我们调查的两个硬问题有关的投票，最优加权游说问题和赢家问题的道奇森选举的问题。关于前者，Christian等人。[CFRS 06]表明，在参数化复杂性的意义上，最优游说是棘手的。我们提供了一个有效的贪心算法，实现了对数近似比这个问题，甚至更一般的变种-最优加权游说。我们证明，基本上没有更好的近似比我们可以证明这个贪心算法。已知确定道奇森获胜者的问题对于NP的并行访问是完全的[HHR 97]。Homan和Hemaspaandra [HH 06]提出了一种有效的贪婪启发式算法，用于找到具有保证成功频率的Dodgson赢家，并且他们的启发式算法是一种“经常自知正确的算法”。"我们证明了，每一个平均在多项式时间内可解的关于均匀分布的分布问题都有一个频繁的自知正确的多项式时间算法。此外，我们还研究了关于Procaccia和Rosenschein的junta分布[PR 07]的正确性概率权重的一些特征。
英文摘要：
We investigate issues related to two hard problems related to voting, the optimal weighted lobbying problem and the winner problem for Dodgson elections. Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is intractable in the sense of parameterized complexity. We provide an efficient greedy algorithm that achieves a logarithmic approximation ratio for this problem and even for a more general variant--optimal weighted lobbying. We prove that essentially no better approximation ratio than ours can be proven for this greedy algorithm. The problem of determining Dodgson winners is known to be complete for parallel access to NP [HHR97]. Homan and Hemaspaandra [HH06] proposed an efficient greedy heuristic for finding Dodgson winners with a guaranteed frequency of success, and their heuristic is a ``frequently self-knowingly correct algorithm.'' We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently self-knowingly correct polynomial-time algorithm. Furthermore, we study some features of probability weight of correctness with respect to Procaccia and Rosenschein's junta distributions [PR07].
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