奇树
Odds-On Trees
摘要：
设R^d -> A是R^d上的一个查询问题，对于该问题存在一个数据结构S，S可以在O（log n）时间内计算R^d中任意查询点q的P（q）。设D是R^d上的概率测度，表示查询的分布。我们描述了一种称为奇数树的数据结构，其大小为O（n^ε），可以用作过滤器，该过滤器可以快速计算R^d中某些查询值q的P（q），并依赖于剩余查询的S。对于奇数树，根据D绘制的点的预期查询时间是O（H*+1），其中H* 是求解P的任何线性决策树的预期成本的下限。奇数树具有许多应用，包括用于2-d中的点定位的分布敏感的数据结构、d维中的多面体中的点测试、简单多边形中的射线射击、多面体中的射线射击，R^d中的最近邻查询、R^d中的超平面排列中的点定位，以及可以在线性决策树模型中解决的许多其他几何搜索问题。一个标准的提升技术扩展这些结果代数决策树的常数度。一个稍微不同的版本的赔率树产生类似的结果，正交搜索问题，可以解决比较树模型。
英文摘要：
Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We describe a data structure called the odds-on tree, of size O(n^ε) that can be used as a filter that quickly computes P(q) for some query values q in R^d and relies on S for the remaining queries. With an odds-on tree, the expected query time for a point drawn according to D is O(H*+1), where H* is a lower-bound on the expected cost of any linear decision tree that solves P. Odds-on trees have a number of applications, including distribution-sensitive data structures for point location in 2-d, point-in-polytope testing in d dimensions, ray shooting in simple polygons, ray shooting in polytopes, nearest-neighbour queries in R^d, point-location in arrangements of hyperplanes in R^d, and many other geometric searching problems that can be solved in the linear-decision tree model. A standard lifting technique extends these results to algebraic decision trees of constant degree. A slightly different version of odds-on trees yields similar results for orthogonal searching problems that can be solved in the comparison tree model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
