In this paper, we calculate the space ExtGL(n)(Ln(λ), Ln(μ)), where GL(n) is the general linear group of degree n over an algebraically closed field of positive characteristic, Ln(λ) and Ln(μ) are rational irreducible GL(n)-modules with highest weights λ and μ respectively, the restriction of Ln(λ) to any Levi subgroup of GL(n) is semisimple, λ is a p-restricted weight and μ does not strictly d...

Selfish behavior of nodes of a network such as sensors of a geographically distributed sensor network, each of which owned and operated by a different stakeholder may lead to a game theoretic setting called “selfish routing”. The fact that every node strictly aims at maximizing its own utility can cause degradations of social welfare. An issue of concern would be the quantitative measure of thi...

The Multicommodity Flow Problem (MCFP) considers the efficient routing of commodities from their origins to their destinations, subject to capacity restrictions and edge costs. This paper studies the NP-hard Minimum Cost Multicommodity k-splittable Flow Problem in which each commodity may use at most k paths between its origin and its destination. The problem has applications in transportation ...

Congestion games come up often in practice they represent our drives to work in the morning, the performance of factories under load, and the routing of packets through computer networks. In addition, all of these instances involve uncertainty. In the automobile traffic model, this uncertainty can come from the random assortment of drivers on the road at one time, but also the random interactio...

The Internet domain name system (DNS) uses rotation of address lists to perform load distribution among replicated servers. We model this kind of load balancing mechanism in form of a set of request streams with different rates that should be mapped to a set of servers. Rotating a list of length k corresponds to breaking streams into k equally sized pieces. We compare this and other strategies ...

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A recent paradigm put forth by Boyle et al. (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms correlated (pseudo)randomness, using minimal interactions followed solely local computations, yielding silent secure two-party computation protocols. This extended $$N $$ -party programmable PCG’s. Previous works construct...

Consider an atomic splittable congestion game played on a parallel-link graph with player-specific cost functions. Richman and Shimkin proved in 2007 that the equilibrium is unique when the cost functions are continuous, increasing, and strictly convex. It allows to define a function ~e(·) mapping any demand vector to the unique corresponding equilibrium. The general question we address in this...

We consider the problem of maintaining aggregates over recent elements of a massive data stream. Motivated by applications involving network data, we consider asynchronous data streams, where the observed order of data may be different from the order in which the data was generated. The set of recent elements is modeled as a sliding timestamp window of the stream, whose elements are changing co...