Text sparsification via local maxima

Text Sparsification via Local Maxima

In this paper we investigate some properties and algorithms related to a text sparsification technique based on the identification of local maxima in the given string. As the number of local maxima depends on the order assigned to the alphabet symbols, we first consider the case in which the order can be chosen in an arbitrary way. We show that looking for an order that minimizes the number of ...

Graph Sparsification via Refinement Sampling

A graph G(V,E) is an ǫ-sparsification of G for some ǫ > 0, if every (weighted) cut in G is within (1 ± ǫ) of the corresponding cut in G. A celebrated result of Benczúr and Karger shows that for every undirected graph G, an ǫ-sparsification with O(n log n/ǫ) edges can be constructed in O(m log n) time. The notion of cut-preserving graph sparsification has played an important role in speeding up ...

Matrix sparsification via the Khintchine inequality

Given a matrix A ∈ Rn×n, we present a simple, element-wise sparsification algorithm that zeroes out all sufficiently small elements of A, keeps all sufficiently large elements of A, and retains some of the remaining elements with probabilities proportional to the square of their magnitudes. We analyze the approximation accuracy of the proposed algorithm using a powerful inequality bounding the ...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Local Maxima of Quadratic Boolean Functions

Combinatorics, Probability and Computing / Volume 25 / Issue 04 / July 2016, pp 633 640 DOI: 10.1017/S0963548315000322, Published online: 21 December 2015 Link to this article: http://journals.cambridge.org/abstract_S0963548315000322 How to cite this article: HUNTER SPINK (2016). Local Maxima of Quadratic Boolean Functions. Combinatorics, Probability and Computing, 25, pp 633-640 doi:10.1017/S0...