In the 2D point searching problem, our goal is to preprocess n points P = {p1, . . . , pn} in the plane so that, for an online sequence of query points q1, . . . qm, we can quickly determine which (if any) of the elements of P are equal to each query point qi. This problem can be solved in O(log n) time by mapping the problem down to one dimension. We present a data structure that is optimized ...

Many query suggestion techniques have been proposed to better capture user intent and to improve search effectiveness. However, most of these methods make use of query logs which are not readily available to the research community. Anchor text, on the other hand, is widely available and has proven useful for many tasks. In this paper, we investigate the problem of query suggestion via random wa...

We consider the dynamic two-dimensional maxima query problem. Let P be a set of n points in the plane. A point is maximal if it is not dominated by any other point in P . We describe two data structures that support the reporting of the t maximal points that dominate a given query point, and allow for insertions and deletions of points in P . In the pointer machine model we present a linear spa...

The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string S of size N compressed by a context-free grammar of size n that answers fingerprint queries. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i, j]...

Given a pattern P and a text T , both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of P occurs in T . The indexed version of this problem, i.e., preprocessing a string to efficiently answer such permutation queries, is hard and has been studied in the last few years. Currently the best bounds for this problem are O(n/ log...

We give a $(1+\epsilon)$-approximate distance oracle with $O(1)$ query time for an undirected planar graph $G$ with $n$ vertices and non-negative edge lengths. For $\epsilon>0$ and any two vertices $u$ and $v$ in $G$, our oracle gives a distance $\tilde{d}(u,v)$ with stretch $(1+\epsilon)$ in $O(1)$ time. The oracle has size $O(n\log n ((\log n)/\epsilon+f(\epsilon)))$ and pre-processing time $...

Given a matrix of size N , two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique—the discrepancy properties of Fibonacci lattices—we give an indexing data structure for 2...

We present an optimal data structure for submatrix maximum queries in n×nMonge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(log logn) time, as well as a matching lower bound, showing that O(log log n) q...

One of the most important issues in the post-genomic molecular biology is the analysis of protein three-dimensional (3-D) structures, and searching over the 3-D structure databases of them is becoming more and more important. The root mean square deviation (RMSD) is the most popular similarity measure for comparing two molecular structures. In this article, we propose new theoretically and prac...