Bipartite graph structures for efficient balancing of heterogeneous loads

International audienceThis paper considers large scale distributed content service platforms, such as peer-to-peer video-on-demand systems. Such systems feature two basic resources, namely storage and bandwidth. Their efficiency critically depends on two factors: (i) content replication within servers, and (ii) how incoming service requests are matched to servers holding requested content. To inform the corresponding design choices, we make the following contributions. We first show that, for underloaded systems, so-called proportional content placement with a simple greedy strategy for matching requests to servers ensures full system efficiency provided storage size grows logarithmically with the system size. However, for constant storage size, this strategy undergoes a phase transition with severe loss of efficiency as system load approaches criticality. To better understand the role of the matching strategy in this performance degradation, we characterize the asymptotic system efficiency under an optimal matching policy. Our analysis shows that -in contrast to greedy matching- optimal matching incurs an inefficiency that is exponentially small in the server storage size, even at critical system loads. It further allows a characterization of content replication policies that minimize the inefficiency. These optimal policies, which differ markedly from proportional placement, have a simple structure which makes them implementable in practice. On the methodological side, our analysis of matching performance uses the theory of local weak limits of random graphs, and highlights a novel characterization of matching numbers in bipartite graphs, which may both be of independent interest

The state of peer-to-peer network simulators

Networking research often relies on simulation in order to test and evaluate new ideas. An important requirement of this process is that results must be reproducible so that other researchers can replicate, validate and extend existing work. We look at the landscape of simulators for research in peer-to-peer (P2P) networks by conducting a survey of a combined total of over 280 papers from before and after 2007 (the year of the last survey in this area), and comment on the large quantity of research using bespoke, closed-source simulators. We propose a set of criteria that P2P simulators should meet, and poll the P2P research community for their agreement. We aim to drive the community towards performing their experiments on simulators that allow for others to validate their results

Efficient CNF Encoding of Boolean Cardinality Constraints

In this paper, we address the encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications. The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers. We prove the practical efficiency of this encoding on some problems arising in discrete tomography that involve many cardinality constraints. This encoding is also used together with a trivial variable elimination in order to re-encode parity learning benchmarks so that a simple Davis and Putnam procedure can solve them

Non Uniform Selection of Solutions for Upper Bounding the 3-SAT Threshold

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