奇偶对策Divide-et-Impera算法的鲁棒指数最坏情况
Robust Exponential Worst Cases for Divide-et-Impera Algorithms for Parity Games
摘要：
McNaughton-Zielonka divide et impera算法是文献中用于确定奇偶博弈中的获胜者的最简单和最灵活的方法。尽管其理论上的最坏情况下的复杂性和负面声誉作为一个效率低下的算法在实践中，它已被证明是最好的技术之一，为解决这类游戏。此外，它被证明是抵抗下界攻击，甚至超过战略改进的方法，直到最近的一个家庭的游戏，该算法需要指数时间已由弗里德曼提供。对该族的简单分析表明，一个简单的记忆技术可以帮助算法在多项式时间内求解该族。同样的结果也可以通过利用文献中提出的基于支配分解技术的方法来实现。这些意见提出了一个问题，动态规划和游戏分解技术的适当组合，可以改善指数最坏情况下的原始算法。在本文中，我们回答这个问题否定的，通过提供一个强大的指数最坏的情况下，表明没有交织的上述技术可以帮助减轻指数性质的划分等impera方法。
英文摘要：
The McNaughton-Zielonka divide et impera algorithm is the simplest and most flexible approach available in the literature for determining the winner in a parity game. Despite its theoretical worst-case complexity and the negative reputation as a poorly effective algorithm in practice, it has been shown to rank among the best techniques for the solution of such games. Also, it proved to be resistant to a lower bound attack, even more than the strategy improvements approaches, and only recently a family of games on which the algorithm requires exponential time has been provided by Friedmann. An easy analysis of this family shows that a simple memoization technique can help the algorithm solve the family in polynomial time. The same result can also be achieved by exploiting an approach based on the dominion-decomposition techniques proposed in the literature. These observations raise the question whether a suitable combination of dynamic programming and game-decomposition techniques can improve on the exponential worst case of the original algorithm. In this paper we answer this question negatively, by providing a robustly exponential worst case, showing that no intertwining of the above mentioned techniques can help mitigating the exponential nature of the divide et impera approaches.
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