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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)

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)

- Matthew Skala
- 2013

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)

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)

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)

- Luis Barba, Stephane Durocher, Robert Fraser, Ferran Hurtado, Saeed Mehrabi, Debajyoti Mondal +3 others
- CCCG
- 2013

• Given a coloured point set, where colours are in {1,…,t} • Given a query c=(c 1 ,…,c t) (and define í µí± = í µí±_í µí± í µí±) • Does there exist an axis aligned rectangle containing a set of points satisfying the query exactly?

- Reza Dorrigiv, Stephane Durocher, Arash Farzan, Robert Fraser, Alejandro López-Ortiz, J. Ian Munro +2 others
- WADS
- 2009

Given a simple polygon P , we consider the problem of finding a convex polygon Q contained in P that minimizes H(P, Q), where H denotes the Hausdorff distance. We call such a polygon Q a Hausdorff core of P. We describe polynomial-time approximations for both the minimization and decision versions of the Hausdorff core problem, and we provide an argument… (More)