Above is the famous Fekete’s lemma which demonstrates that the ratio of subadditive sequence (an) to n tends to a limit as n approaches infinity. This lemma is quite crucial in the field of subadditive ergodic theorems because it gives mathematicians some general ideas and guidelines in the non-random setting and leads to analogous discovery in the random setting. Kingman’s Subadditive Ergodic ...

Given a nonempty abstract set X, and a covering class C, and a finite, finitely subadditive outer measure ν, we construct an outer measure ν and investigate conditions for ν to be submodular. We then consider several other set functions associated with ν and obtain conditions for equality of these functions on the lattice generated by C. Lastly, we describe a construction of a finite, finitely ...

All the functions we consider are set functions defined over subsets of a ground set N . Definition 1. A function f : 2 → R is monotone iff: ∀S ⊆ T ⊆ N, f(S) ≤ f(T ) Definition 2. For f : 2 → R and S ⊆ N , the marginal contribution to S is the function fS defined by: ∀T ⊆ N, fS(T ) = f(S ∪ T )− f(S) When there is no ambiguity, we write fS(e) instead of fS({e}) for e ∈ N , S + e instead of S ∪ {...

Budget feasible mechanism design is the study of procurement combinatorial auctions in which the sellers have private costs to produce items, and the buyer (auctioneer) aims to maximize her valuation function on a subset of purchased items under the budget constraint on the total payment. One of the most important questions in the field is “which valuation domains admit truthful budget feasible...

In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M and N are denote to Arithmetic, Geometric and Harmonic means and h is a non-negative superadditive or subadditive function.

We study algorithms for the sliding-window model, an important variant of data-stream in which goal is to compute some function a fixed-length suffix stream. extend smooth-histogram framework Braverman and Ostrovsky (FOCS 2007) almost-smooth functions, includes all subadditive functions. Specifically, we show that if can be \(\left( 1+{{\varepsilon }}\right) \)-approximated insertion-only strea...

A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.

Tail asymptotics for the supremum of an independent subadditive process are obtained as a function of the logarithmic moment generating function. We use this analysis to obtain large deviations results for queueing networks in their stationary regime. In the particular case of (max,plus)-linear recursions, the rate of exponential decay of the stationary solution can be explicitly computed.