P∈Pi P∋e fi,P ≤ ce ∀e fi,P ≥ 0 Dual 1 solves the max-sum multi-commodity flow problem: ce represents the capacity of an edge, and fi,P is the amount of flow directed from si to ti along the path P . The LP tries to maximize the total amount of commodity flow. Lemma 17.1.1 Multicut is always larger than the corresponding max-sum multi-commodity flow. Lemma 17.1.2 Multicut is at most O(logK) time...

The traditional multi-commodity ow problem assumes a given ow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity ow network-design problem: given a set of multi-commodity ow demands, nd a network subject to certain constraints such that the commodities can be maximally routed. This paper focuses on the case whe...

We have designed and implemented a virtual machine monitor that virtualizes a sharedmemory multi-processor machine on a commodity cluster. This functionality greatly simplifies utilization of commodity clusters. For example, it enables parallel applications for sharedmemory multi-processor systems to run on clusters without any change of the applications. Moreover, commodity operating systems t...

Multiple coverings of the farthest-off points ((R,μ)-MCF codes) and the corresponding (ρ, μ)-saturating sets in projective spaces PG(N, q) are considered. We propose some methods which allow us to obtain new small (1, μ)-saturating sets and short (2, μ)-MCF codes with μ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1+1/cq, c ≥ 1). In par...

Constitutive laws for multi-component fluids (MCF) is one of the thorniest problems in science. Two questions explored here are: how to ensure that these relations reduce to accepted forms when all but one of the constituents vanishes; and what constraints does the Second Law impose on the dynamics of viscous fluids at different temperatures? The analysis suggests an alternative to the metaphys...