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We consider range queries that search for low-frequency elements (least frequent elements and $$\alpha $$ α -minorities) in arrays. An $$\alpha $$ α -minority of a query range has multiplicity no greater than an $$\alpha $$ α fraction of the elements in the range. Our data structure for the least frequent element range query problem requires $$O(n)$$ O ( n… (More)

Given an array A of size n, we consider the problem of answering range majority queries: given a query range [i..j] where 1 ≤ i ≤ j ≤ n, return the majority element of the subarray A[i..j] if it exists. We describe a linear space data structure that answers range majority queries in constant time. We further generalize this problem by defining range… (More)

Distance permutation indexes support fast proximity searching in high-dimensional metric spaces. Given some fixed reference sites, for each point in a database the index stores a permutation naming the closest site, the second-closest, and so on. We examine how many distinct permutations can occur as a function of the number of sites and the size of the… (More)

Array range queries are of current interest in the field of data structures. Given an array of numbers or arbitrary elements, the general array range query problem is to build a data structure that can efficiently answer queries of a given type stated in terms of an interval of the indices. The specific query type might be for the minimum element in the… (More)

We present the first adaptive data structure for two-dimensional orthogonal range search. Our data structure is adaptive in the sense that it gives improved search performance for data with more inherent sortedness. Given n points in the plane, it can answer range queries in O(k log n+m) time, where m is the number of points in the output and k is the… (More)

We present $$O(n)$$ O ( n ) -space data structures to support various range frequency queries on a given array $$A[0:n-1]$$ A [ 0 : n - 1 ] or tree $$T$$ T with $$n$$ n nodes. Given a query consisting of an arbitrary pair of pre-order rank indices $$(i,j)$$ ( i , j ) , our data structures return a least frequent element, mode, $$\alpha $$ α -minority, or… (More)

Data structures for similarity search are commonly evaluated on data in vector spaces, but distance-based data structures are also applicable to non-vector spaces with no natural concept of dimen-sionality. The intrinsic dimensionality statistic of Chávez and Navarro provides a way to compare the performance of similarity indexing and search algorithms… (More)

Constructing an encoding of a concept lattice using short bit vectors allows for efficient computation of join operations on the lattice. Join is the central operation any unification-based parser must support. We extend the traditional bit vector encoding , which represents join failure using the zero vector, to count any vector with less than a fixed… (More)

We consider how to preprocess n colored points in the plane such that later, given a multiset of colors, we can quickly find an axis-aligned rectangle containing a subset of the points with exactly those colors, if one exists. We first give an index that uses o(n 4) space and o(n) query time when there are O(1) distinct colors. We then restrict our… (More)

Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple , fast, and highly practical data structure for answering AFN queries in high-dimensional Euclidean space. We build on the technique of In-dyk (SODA 2003),… (More)