硬度减半结果
Hardness Results for Consensus-Halving
摘要：
我们研究了将一个对象分成两部分的共识减半问题，使得每个$n$代理对这两部分具有相等的估值。$ε$近似共识减半问题允许每个代理在部分值上具有$ε$差异。我们证明了使用$n$切割计算$ε$ -近似共识减半解是PPA，并且是PPAD-困难的，其中$ε$是某个正常数;当我们允许恒定数量的额外切割时，问题仍然是PPAD-困难的。判定该问题是否存在$n-1$割的解是NP困难的。作为我们的结果的推论，我们得到的近似计算版本的连续项链分裂问题是PPAD困难的部分$t$的数量是2。
英文摘要：
We study the consensus-halving problem of dividing an object into two portions, such that each of $n$ agents has equal valuation for the two portions. The $ε$-approximate consensus-halving problem allows each agent to have an $ε$ discrepancy on the values of the portions. We prove that computing $ε$-approximate consensus-halving solution using $n$ cuts is in PPA, and is PPAD-hard, where $ε$ is some positive constant; the problem remains PPAD-hard when we allow a constant number of additional cuts. It is NP-hard to decide whether a solution with $n-1$ cuts exists for the problem. As a corollary of our results, we obtain that the approximate computational version of the Continuous Necklace Splitting Problem is PPAD-hard when the number of portions $t$ is two.
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