图的性质的Evasiveness与拓扑不动点定理
Evasiveness of Graph Properties and Topological Fixed-Point Theorems
摘要：
许多图形属性（例如，连通性，包含一个完整的子图）是已知的难以检查。在决策树模型中，算法的成本是由它查询的图中的边的数量来衡量的。R.卡普在20世纪70年代初推测，所有单调图属性都是回避的--也就是说，任何计算单调图属性的算法都必须在最坏的情况下检查所有边。这个猜想还没有得到证实，但已经取得了很大的进展。从1984年Kahn，Saks和Sturtevant的工作开始，拓扑方法被应用于证明Karp猜想的部分结果。本文是这些拓扑方法的教程。我给一个完全独立的帐户的中央证明文件的卡恩，萨克斯，和Sturtevant，没有先验知识的拓扑假设。我还简要地回顾了一些关于回避的最新研究结果。
英文摘要：
Many graph properties (e.g., connectedness, containing a complete subgraph) are known to be difficult to check. In a decision-tree model, the cost of an algorithm is measured by the number of edges in the graph that it queries. R. Karp conjectured in the early 1970s that all monotone graph properties are evasive -- that is, any algorithm which computes a monotone graph property must check all edges in the worst case. This conjecture is unproven, but a lot of progress has been made. Starting with the work of Kahn, Saks, and Sturtevant in 1984, topological methods have been applied to prove partial results on the Karp conjecture. This text is a tutorial on these topological methods. I give a fully self-contained account of the central proofs from the paper of Kahn, Saks, and Sturtevant, with no prior knowledge of topology assumed. I also briefly survey some of the more recent results on evasiveness.
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