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- Kasper Green Larsen, J. Ian Munro, Jesper Sindahl Nielsen, Sharma V. Thankachan
- Theor. Comput. Sci.
- 2014

Let D = {d1, d2, ..., dD} be a collection of D string documents of n characters in total. The two-pattern matching problems ask to index D for answering the following queries efficiently. – report/count the unique documents containing P1 and P2. – report/count the unique documents containing P1, but not P2. Here P1 and P2 represent input patterns of length… (More)

- J. Ian Munro, Gonzalo Navarro, Jesper Sindahl Nielsen, Rahul Shah, Sharma V. Thankachan
- Algorithmica
- 2014

Let $$\mathcal {D} = \{\mathsf {T}_1,\mathsf {T}_2, \ldots ,\mathsf {T}_D\}$$ D = { T 1 , T 2 , … , T D } be a collection of D string documents of n characters in total, that are drawn from an alphabet set $$\varSigma =[\sigma ]$$ Σ = [ σ ] . The top-k document retrieval problem is to preprocess $$\mathcal{D}$$ D into a data structure that, given a query… (More)

Sorting n integers in the word-RAM model is a fundamental problem and a long-standing open problem is whether integer sorting is possible in linear time when the word size is ω(logn). In this paper we give an algorithm for sorting integers in expected linear time when the word size is Ω(log n log logn). Previously expected linear time sorting was only… (More)

We address the problem of creating a dictionary with the finger search property in the strict implicit model, where no information is stored between operations, except the array of elements. We show that for any implicit dictionary supporting finger searches in q(t) = Ω(log t) time, the time to move the finger to another element is Ω(q−1(logn)), where t is… (More)

- Peyman Afshani, Jesper Sindahl Nielsen
- ICALP
- 2016

We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower bounds that cannot be obtained in any other known model of computation with the current techniques. Often our lower… (More)

The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements n – here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized O(1) time Insert and O(logn) time ExtractMin operations,… (More)

- Peyman Afshani, Edvin Berglin, Ingo van Duijn, Jesper Sindahl Nielsen
- Symposium on Computational Geometry
- 2016

In the Line Cover problem a set of n points is given and the task is to cover the points using either the minimum number of lines or at most k lines. In Curve Cover, a generalization of Line Cover, the task is to cover the points using curves with d degrees of freedom. Another generalization is the Hyperplane Cover problem where points in d-dimensional… (More)

The k-Means clustering problem on n points is NP-Hard for any dimension d ≥ 2, however, for the 1D case there exist exact polynomial time algorithms. Previous literature reported an O(kn) time dynamic programming algorithm that uses O(kn) space. We present a new algorithm computing the optimal clustering in only O(kn) time using linear space. For k = Ω(lg… (More)

Computing the discrete Fourier transform is one of the most important in applied computer science, with applications in fields as diverse as seismology, signal analysis, and various branches of engineering. A great many algorithms exist for quickly computing different variations of the transform – fast Fourier transforms, or FFTs. Because of their practical… (More)

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