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- Timothy M. Chan, Stephane Durocher, Matthew Skala, Bryan T. Wilkinson
- Algorithmica
- 2012

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)

- Stephane Durocher, Meng He, J. Ian Munro, Patrick K. Nicholson, Matthew Skala
- Inf. Comput.
- 2011

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)

- Matthew Skala
- 2008 IEEE 24th International Conference on Data…
- 2008

A distance permutation index supports fast proximity searching in a high-dimensional metric space. 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)

- Matthew Skala
- 2013

- Diego Arroyuelo, Francisco Claude, +7 authors Matthew Skala
- Theor. Comput. Sci.
- 2009

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
- SPIRE
- 2005

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)

- Matthew Skala
- Space-Efficient Data Structures, Streams, and…
- 2013

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)

- Stephane Durocher, Rahul Shah, Matthew Skala, Sharma V. Thankachan
- Algorithmica
- 2013

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)

- Luis Barba, Stephane Durocher, +6 authors Mohammad Abdul Wahid
- 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, +5 authors Matthew Skala
- 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)