Motivation Want to learn a combinatorial parameter of a graph: the maximum matching size the independence number α(G), the minimum vertex cover size, the minimum dominating set size Krzysztof Onak – Sublinear Graph Approximation Algorithms – p. 2/32 Motivation Want to learn a combinatorial parameter of a graph: the maximum matching size the independence number α(G), the minimum vertex cover siz...

A distance labeling scheme labels the n nodes of a graph with binary strings such that, given the labels of any two nodes, one can determine the distance in the graph between the two nodes by looking only at the labels. A D-preserving distance labeling scheme only returns precise distances between pairs of nodes that are at distance at least D from each other. In this paper we consider distance...

In this paper we survey recent advances in the area of sublinear-time algorithms.

In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria fo...

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random Gexpectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent li...

Recently, Dimitrov et. al. [4] proposed a novel algorithm for scalar multiplication of points on elliptic Koblitz curves that requires a provably sublinear number of point additions in the size of the scalar. Following some ideas used by this article, most notably double-base expansions for integers, we generalize their methods to hyperelliptic Koblitz curves of arbitrary genus over any nite el...

The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...

Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a very small portion of the input. We discuss the types of answers that one can hope to achieve in this setting.

Let 0 < a < b < ∞, and for each edge e of Zd let ωe = a or ωe = b, each with probability 1/2, independently. This induces a random metric distω on the vertices of Z d, called first passage percolation. We prove that for d > 1 the distance distω(0, v) from the origin to a vertex v, |v| > 2, has variance bounded by C |v|/ log |v|, where C = C(a, b, d) is a constant which may only depend on a, b a...

The present paper deals with the subject of approximate string matching and demonstrates how Chang and Lawler [CL94] conceived a new sublinear time algorithm out of ideas that had previously been known. The problem is to find all locations in a text of length n over a b-letter alphabet where a pattern of length m occurs with up to k differences (substitutions, insertions, deletions). The algori...