Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are considered is property testing. There are several interesting contexts where one can test properties in sublinear time. A canonical example is graph colorability. To...

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our sublinear expectation, we give a simple construction, in a quasi-sure sense, of the (linear) conditional expectations, and hence give a representation for the c...

This paper studies K-sublinear inequalities, a class of inequalities with strong relations to K-minimal inequalities for disjunctive conic sets. We establish a stronger result on the sufficiency of K-sublinear inequalities. That is, we show that when K is the nonnegative orthant or the second-order cone, K-sublinear inequalities together with the original conic constraint are always sufficient ...

A context-free grammar G is ambiguous if there is a word that can be generated by G with at least two different derivation trees. Ambiguous grammars are often distinguished by their degree of ambiguity, which is the maximal number of derivation trees for the words generated by them. If there is no such upper bound G is said to be ambiguous of infinite degree. By considering how many derivation ...

We develop a randomized approximation algorithm for the classical maximum coverage problem, which given a list of sets A1, A2, · · · , An and integer parameter k, select k sets Ai 1 , Ai 2 , · · · , Ai k for maximum union Ai 1 ∪ Ai 2 ∪ · · · ∪ Ai k. In our algorithm, each input set Ai is a black box that can provide its size |Ai|, generate a random element of Ai, and answer the membership query...

Consider the Emden-Fowler sublinear dynamic equation (0.1) x(t) + p(t)x(σ(t)) = 0, where p ∈ C(T, R), where T is a time scale, 0 < α < 1, α is the quotient of odd positive integers. When p(t) is allowed to take on negative values, we obtain a Belohorec-type oscillation theorem for (0.1). As an application, we get that the sublinear difference equation (0.2) ∆x(n) + p(n)x(n+ 1) = 0, is oscillato...