用于着色范围和前缀报告的I/O高效数据结构
I/O-Efficient Data Structures for Colored Range and Prefix Reporting
摘要：
受信息检索应用的启发，我们考虑了秩空间中的一维着色范围报告问题。目标是为集合C_1，...，C_m \subseteq {1，.，sigma}，其支持以下类型的查询：给定索引a、b，报告集合Union_{a <= i <= b} C_i。我们在I/O模型中研究了这个问题，并证明了存在一个最优线性空间数据结构，它能在O（1+k/B）I/O中回答查询，其中k表示输出大小，B表示磁盘块大小.事实上，我们得到了相同的三边正交范围报告的更难的问题。在这个问题中，我们要对秩空间中的一组n个二维点进行预处理，使得可以报告形式为[x_1，x_2] x（-infinity，y]的查询矩形内的所有点。这个问题的最佳前界要么是O（n lg^2_Bn）空间和O（1+k/B）查询I/O，要么是O（n）空间和O（lg^（h）_Bn +k/B）查询I/O，其中lg^（h）_Bn是以B为底的对数迭代h次，对于任何常数整数h。前面的边界都是在不可分割假设下实现的，而我们的解决方案利用了底层机器的全部功能。因此，打破不可分割性假设为我们提供了更清晰和最优的边界。我们的研究结果也意味着一个最佳的解决方案，下面的彩色前缀报告问题。给定一组字符串S，每个磁盘块的长度为O（1），函数c：S -> 2^{1，.，sigma}，支持以下类型的查询：给定字符串p，报告集合Union_{x in S intersection p*} c（x），其中p* 表示前缀为p的字符串集合。最后，我们考虑了此结果的top-k扩展的可能性，并在允许非阻塞I/O的模型中提出了一个简单的解决方案。
英文摘要：
Motivated by information retrieval applications, we consider the one-dimensional colored range reporting problem in rank space. The goal is to build a static data structure for sets C_1,...,C_m \subseteq {1,...,sigma} that supports queries of the kind: Given indices a,b, report the set Union_{a <= i <= b} C_i. We study the problem in the I/O model, and show that there exists an optimal linear-space data structure that answers queries in O(1+k/B) I/Os, where k denotes the output size and B the disk block size in words. In fact, we obtain the same bound for the harder problem of three-sided orthogonal range reporting. In this problem, we are to preprocess a set of n two-dimensional points in rank space, such that all points inside a query rectangle of the form [x_1,x_2] x (-infinity,y] can be reported. The best previous bounds for this problem is either O(n lg^2_B n) space and O(1+k/B) query I/Os, or O(n) space and O(lg^(h)_B n +k/B) query I/Os, where lg^(h)_B n is the base B logarithm iterated h times, for any constant integer h. The previous bounds are both achieved under the indivisibility assumption, while our solution exploits the full capabilities of the underlying machine. Breaking the indivisibility assumption thus provides us with cleaner and optimal bounds. Our results also imply an optimal solution to the following colored prefix reporting problem. Given a set S of strings, each O(1) disk blocks in length, and a function c: S -> 2^{1,...,sigma}, support queries of the kind: Given a string p, report the set Union_{x in S intersection p*} c(x), where p* denotes the set of strings with prefix p. Finally, we consider the possibility of top-k extensions of this result, and present a simple solution in a model that allows non-blocked I/O.
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。
