We conduct a study on the problem of fair allocation indivisible goods when maximin share [1] is used as measure fairness. Most current studies this notion are limited to case that valuations additive. In paper, we go beyond additive and consider cases submodular, fractionally subadditive, subadditive. give constant approximation guarantees for agents with submodular XOS valuations, logarithmic...

Let ,: X_T+ X be a semiflow on a compact metric space X. A function F: X_T+ X is subadditive with respect to , if F(x, t+s) F(x, t)+F(,(x, t), s). We define the maximal growth rate of F to be supx # X lim supt (1 t) F(x, t). This growth rate is shown to equal the maximal growth rate of the subadditive function restricted to the minimal center of attraction of the semiflow. Applications to Birkh...

An elementary theorem on subadditive sequences provides the key to a far-reaching theory of subadditive processes. One important instance of this theory is the limit theory for products of stationary random matrices. This paper shows that the subadditive inequality that governs the log of the norm of ordinary matrix products also governs other functions of several generalized matrix products. T...

Negotiation among multiple agents remains an important topic of research in Distributed Artiicial Intelligence (DAI). Most previous work on this subject, however, has focused on bilateral negotiation, deals that are reached between two agents. There has also been research on n-agent agreement which has considered \consensus mechanisms" (such as voting), that allow the full group to coordinate i...

The in…nite combinatorics here give statements in which, from some sequence, an in…nite subsequence will satisfy some condition – for example, belong to some speci…ed set. Our results give such statements generically –that is, for ‘nearly all’points, or as we shall say, for quasi all points –all o¤ a null set in the measure case, or all o¤ a meagre set in the category case. The prototypical res...

We study combinatorial auctions where each item is sold separately but simultaneously via a second price auction. We ask whether it is possible to efficiently compute in this game a pure Nash equilibrium with social welfare close to the optimal one. We show that when the valuations of the bidders are submodular, in many interesting settings (e.g., constant number of bidders, budget additive bid...

Recent work on decision tree pruning [1] has brought to the attention of the machine learning community the fact that, in classification problems, the use of subadditive penalties in cost-complexity pruning has a stronger theoretical basis than the usual additive penalty terms. We implement cost-complexity pruning algorithms with general size-dependent penalties to confirm the results of [1]. N...

The classical Hlawka inequality possesses deep connections with zonotopes and zonoids in convex geometry, has been related to Minkowski space. We introduce Type-1 Type-2 quantities, establish a Hlawka-type relation between them, which connects vast number of strikingly different variants the inequalities, such as Serre's reverse future cone space, for subadditive function on abelian group by Re...

The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super-and sub-additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric inequalities and cannot be reduced to equalities. Rather, the pseudo-additivity relation is a functional equation that determines the functional forms of the random ...

The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion ofthe theory ofinner measures, their construction, and the relationship oftheir prop...