论文标题
PPA的恒定不XiBIBIBIBIBITIS
Constant Inapproximability for PPA
论文作者
论文摘要
在$ \ varepsilon $ -consensus-halafore问题中，我们得到了$ n $概率度量$ v_1，\ dots，v_n $，interval $ r = [0,1] $，目标是将$ r $ $ r $分为两个部分$ r^+$ r^+$和$ r^ - $ r^ - $ r^ - 最多使用$ n $ cuts $ n $ cuts $ | v_i | \ leq \ varepsilon $用于所有$ i $。这个基本的公平划分问题是PPA类证明是完整的第一个自然问题，并且通过从中减少来获得其他自然问题的所有随后的PPA完整性结果。 我们表明，即使参数$ \ varepsilon $是一个常数，即使$ \ varepsilon $ -consensus-halving也是PPA完成的。实际上，我们证明这适用于任何常数$ \ varepsilon <1/5 $。结果，我们为所有已知的天然PPA完整问题获得了恒定的不XiBIBITISION结果，包括项链分裂，离散的汉姆 - 桑德里奇问题，披萨共享问题的两个变体以及在周期和路径中找到公平的独立集。
In the $\varepsilon$-Consensus-Halving problem, we are given $n$ probability measures $v_1, \dots, v_n$ on the interval $R = [0,1]$, and the goal is to partition $R$ into two parts $R^+$ and $R^-$ using at most $n$ cuts, so that $|v_i(R^+) - v_i(R^-)| \leq \varepsilon$ for all $i$. This fundamental fair division problem was the first natural problem shown to be complete for the class PPA, and all subsequent PPA-completeness results for other natural problems have been obtained by reducing from it. We show that $\varepsilon$-Consensus-Halving is PPA-complete even when the parameter $\varepsilon$ is a constant. In fact, we prove that this holds for any constant $\varepsilon < 1/5$. As a result, we obtain constant inapproximability results for all known natural PPA-complete problems, including Necklace-Splitting, the Discrete-Ham-Sandwich problem, two variants of the pizza sharing problem, and for finding fair independent sets in cycles and paths.
