Virtual Machine (VM) placement has to carefully consider the aggregated resource consumption of co-located VMs in order to obey service level agreements at lower possible cost. In this paper, we focus on satisfying the traffic demands of the VMs in addition to CPU and memory requirements. This is a much more complex problem both due to its quadratic nature (being the communication between a pair of VMs) and since it involves many factors beyond the physical host, like the network topologies and the routing scheme. Moreover, traffic patterns may vary over time and predicting the resulting effect on the actual available bandwidth between hosts within the data center is extremely difficult.We address this problem by trying to allocate a placement that not only satisfies the predicted communication demand but is also resilient to demand time-variations. This gives rise to a new optimization problem that we call the Min Cut Ratio-aware VM Placement (MCRVMP). The general MCRVMP problem is NPHard; hence, we introduce several heuristics to solve it in reasonable time. We present extensive experimental results, associated with both placement computation and run-time performance under time-varying traffic demands, to show that our heuristics provide good results (compared to the optimal solution) for medium size data centers.

Fischer, Lynch and Paterson showed in a fundamental paper that achieving a distributed agreement is impossible in the presence of one faulty processor. This result was later extended by Moran and Wolfstahl who showed that it holds for any task with a connected input graph and a disconnected decision graph.In this paper we extend that latter result, and in fact we set an exact borderline between solvable and unsolvable tasks, by giving a necessary and sufficient condition for a task to be 1-solvable (that is: solvable in the presence of one faulty processor). Our characterization is purely combinatorial, and involves only relations between the input graph and the output graph, defined by the given task. It provides easy proofs for the non-solvability of tasks, and also provides a universal protocol which solves any task which is found to be solvable by our condition.Using the above characterization, we also derive a novel technique to prove lower bounds on the number of messages that must be sent due to processor failure; specifically, we provide a simple proof that for each fixed N > 2 there exist distributed tasks for N processors, that can be solved in the presence of a faulty processor, but any protocol that solves them must send arbitrarily many messages in the worst case.

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Fischer, Lynch and Paterson showed in a fundamental paper that achieving a distributed agreement for N > I processors is impossible in the presence of one faulty processor. This result was later extended by Moran and Wolfstahl who showed that it holds for any task with a connected input graph and a disconnected decision graph (whcrc a vcrtcx in the input [decision] graph is an N-tuple of input [decision] values of the processors, and there is an edge connecting two vertices if and only if they differ in exactly one component),In this paper we extend that latter result, and in fact we set the exact bordedine between solvable and unsolvable tasks, by giving a necessary and sufficient condition for a task to be solvable in the presence of a faulty processor. We present a universal protocol which solves any task which is found to be solvable by our condition.Using our characterization, we derive a novel technique to prove lower bounds on the number of messages that must be sent due to processor failure; specifically, we show that for each fixed JV > 2 there exist distributed tasks for Iv processors that can be solved in the presence of a faulty processor, but any protocol that solves them must send arbitrarily many messages in the worst case.