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Scheduling has been extensively studied in various disciplines in operations research and wireline networking. However, the unique characteristics of wireless communication systems-namely, timing-varying channel conditions and multiuser diversity-means that new scheduling solutions need to be developed that are specifically tailored for this environment. In this paper, we summarize various opportunistic scheduling schemes that exploit the time-varying nature of the radio environment to improve the spectrum efficiency while maintaining a certain level of satisfaction for each user. We also discuss the advantages and costs associated with opportunistic scheduling, and identify possible future research directions.

We present an "opportunistic" transmission scheduling policy that exploits time-varying channel conditions and maximizes the system performance stochastically under a certain resource allocation constraint. We establish the optimality of the scheduling scheme, and also that every user experiences a performance improvement over any non-opportunistic scheduling policy when users have independent performance values. We demonstrate via simulation results that the scheme is robust to estimation errors, and also works well for nonstationary scenarios, resulting in performance improvements of 20-150% compared with a scheduling scheme that does not take into account channel conditions. Last, we discuss an extension of our opportunistic scheduling scheme to improve "short-term" performance.

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Applications such as e-commerce payment protocols, electronic contract signing, and certified e-mail delivery require that fair exchange be assured. A fair-exchange protocol allows two parties to exchange items in a fair way so that either each party gets the other's item, or neither party does. We describe a novel method of constructing very efficient fair-exchange protocols by distributing the computation of RSA signatures. Specifically, we employ multisignatures based on the RSA-signature scheme. To date, the vast majority of fair-exchange protocols require the use of zero-knowledge proofs, which is the most computationally intensive part of the exchange protocol. Using the intrinsic features of our multisignature model, we construct protocols that require no zero-knowledge proofs in the exchange protocol. Use of zero-knowledge proofs is needed only in the protocol setup phase--this is a one-time cost. Furthermore, our scheme uses multisignatures that are compatible with the underlying standard (single-signer) signature scheme, which makes it possible to readily integrate the fair-exchange feature with existing e-commerce systems. Categories and Subject General TermsAlgorithms, Security, Design KeywordsFair-exchange protocols~ e-commerce, multisignatures, RSA signatures, zero-knowledge proofs.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.

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The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of "the same information" two or more random variables specify about a target random variable. As of yet, none is wholly satisfactory. A palatable measure of intersection information would provide a principled way to quantify slippery concepts, such as synergy. Here, we introduce an intersection information measure based on the Gács-Körner common random variable that is the first to satisfy the coveted target monotonicity property. Our measure is imperfect, too, and we suggest directions for improvement.

Abstract-The problem of choosing a string of actions to optimize an objective function that is string submodular has been considered in [1]. There it is shown that the greedy strategy, consisting of a string of actions that only locally maximizes the step-wise gain in the objective function, achieves at least a (1 − e −1 )-approximation to the optimal strategy. This paper improves this approximation by introducing additional constraints on curvature, namely, total backward curvature, total forward curvature, and elemental forward curvature. We show that if the objective function has total backward curvature σ, then the greedy strategy achieves at least a 1 σ(1 − e −σ )-approximation of the optimal strategy. If the objective function has total forward curvature ǫ, then the greedy strategy achieves at least a (1 − ǫ)-approximation of the optimal strategy. Moreover, we consider a generalization of the diminishing-return property by defining the elemental forward curvature. We also introduce the notion of string-matroid and consider the problem of maximizing the objective function subject to a string-matroid constraint. We investigate two applications of string submodular functions with curvature constraints: 1) choosing a string of actions to maximize the expected fraction of accomplished tasks; and 2) designing a string of measurement matrices such that the information gain is maximized.