分数阶稳定性问题的约化
Reducibility Among Fractional Stability Problems
摘要：
在本文中，我们解决了计算复杂性的一些突出的开放问题与实际应用。以下是我们证明为PPAD完备的问题列表，以及具有实际意义的领域：分数稳定路径问题（FSPP）[21] -互联网路由;平衡博弈的核心[41] -经济学和博弈论; Scarf引理[41] -组合学;超图匹配[1]-社会选择和偏好系统;分数有界预算连接游戏（FBBC）[30] -社交网络;和强分数核[2]-图论。事实上，我们表明，没有完全多项式时间近似方案存在（除非PPAD是在FP）。本文完全是一系列的减少，建立在非平凡的方式在以前的工作中建立的框架。在推导这些简化的过程中，我们创造了两个新的概念-偏好博弈和个性化均衡。整个新的约简集可以表示为一个格子，上面的问题夹在偏好博弈（在“容易”端）和个性化均衡（在“困难”端）之间。我们的完整性结果扩展到自然的近似版本的大多数这些问题。在一个技术说明，我们希望强调我们的新的“连续到离散”减少从精确的个性化平衡到近似个性化的平衡使用线性规划增加了一个特定形式的指数数量的“最小”约束。除了提高我们的剧目PPAD完全的问题，我们希望本文中的概念和技术，找到未来的使用在算法博弈论。
英文摘要：
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance: Fractional Stable Paths Problem (FSPP) [21] - Internet routing; Core of Balanced Games [41] - Economics and Game theory; Scarf's Lemma [41] - Combinatorics; Hypergraph Matching [1]- Social Choice and Preference Systems; Fractional Bounded Budget Connection Games (FBBC) [30] - Social networks; and Strong Fractional Kernel [2]- Graph Theory. In fact, we show that no fully polynomial-time approximation schemes exist (unless PPAD is in FP). This paper is entirely a series of reductions that build in nontrivial ways on the framework established in previous work. In the course of deriving these reductions, we created two new concepts - preference games and personalized equilibria. The entire set of new reductions can be presented as a lattice with the above problems sandwiched between preference games (at the "easy" end) and personalized equilibria (at the "hard" end). Our completeness results extend to natural approximate versions of most of these problems. On a technical note, we wish to highlight our novel "continuous-to-discrete" reduction from exact personalized equilibria to approximate personalized equilibria using a linear program augmented with an exponential number of "min" constraints of a specific form. In addition to enhancing our repertoire of PPAD-complete problems, we expect the concepts and techniques in this paper to find future use in algorithmic game theory.
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