This short note exhibits a truthful-in-expectation O( logm log logm )-approximation mechanism for combinatorial auctions with subadditive bidders that uses polynomial communication.

We study the problem of allocating a set indivisible goods among agents with subadditive valuations in fair and efficient manner. Envy-Freeness up to any good (EFX) is most compelling notion fairness context goods. Although existence EFX not known beyond simple case two valuations, some approximations are exist, namely 1/2-EFX allocation allocations bounded charity. Nash welfare (the geometric ...

The value function of a mixed-integer linear program (MILP) is a function that returns the optimal solution value as a function of the right-hand side. In this paper, we analyze the structure of the value function of a MILP with a single constraint. We show that the value function is uniquely determined by a finite number of break points and at most two slopes. We derive conditions for the valu...

Such inequalities have been then used on general time scales, including discretetime versions of (1) and (2) (see [3]). In the present note we generalize both inequalities (1) and (2) in a different direction, by considering more general retarded inequalities, i.e., by letting the upper limit of the integrals to be C1 nondecreasing functions less than or equal to t (cf. (4) and (10) below). Mor...

In this paper we define the fuzzy integral of a positive, measurable function, with respect to a fuzzy measure. We show that the monotone convergence theorem and Fatou’s lemma are still true in this new setting. We study some of the properties of this integral, and show that it coincides with another fuzzy integral defmed in the literature. Our main result is a convergence theorem, that is in a...

We introduce and study an eigenvalue upper bound p(G) on the maximum cut mc (G) of a weighted graph. The function ~o(G) has several interesting properties that resemble the behaviour of mc (G). The following results are presented. We show that q~ is subadditive with respect to amalgam, and additive with respect to disjoint sum and 1-sum. We prove that ~(G) is never worse that 1.131 mc(G) for a ...

We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of L evy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our...

The effects of vincristine (VCR) in combination with methotrexate (MTX) and other antitumor agents were evaluated by cell growth inhibition assay using a human acute lymphoblastic leukemia cell line (MOLT-3). The data were analyzed with the aid of an isobologram using the concept of an envelope of additivity (G. G. Steel and M. J. Peckman, Int. J. Radiat. Oncol., 5:85-91, 1979). Simultaneous ex...