In a virtualized infrastructure where physical resources are shared, a single physical server failure will terminate several virtual servers and crippling the virtual infrastructures which contained those virtual servers. In the worst case, more failures may cascade from overloading the remaining servers. To guarantee some level of reliability, each virtual infrastructure, at instantiation, should be augmented with backup virtual nodes and links that have sufficient capacities. This ensures that, when physical failures occur, sufficient computing resources are available and the virtual network topology is preserved. However, in doing so, the utilization of the physical infrastructure may be greatly reduced. This can be circumvented if backup resources are pooled and shared across multiple virtual infrastructures, and intelligently embedded in the physical infrastructure. These techniques can reduce the physical footprint of virtual backups while guaranteeing reliability.
Structural fault tolerance (SFT) is the ability of a multiprocessor to reconfigure around faulty processors or links in order to preserve its original processor interconnection structure; In this paper, we focus on the design of SFT multiprocessors that have low switch and link overheads, but can tolerate a very large number of processor faults on the average. Most previous work has concentrated on deterministic k-fault-tolerant (k-FT) designs in which exactly k spare processors and some spare switches and links are added to construct multiprocessors that can tolerate any k processor faults. However, after k faults are reconfigured around, much of the extra links and switches can remain unutilized. It is possible within the basic node-covering framework, which was introduced by Dutt and Hayes as an efficient k-FT design method, to design FT multiprocessors that have the same amount of switches and links as, say, a two-FT deterministic design, but have s spare processors, where s spl Gt 2, so that, on the average, k= spl Theta (s) (k spl les s) processor failures can be reconfigured around. Such designs utilize the spare link and switch capacity very efficiently, and are called probabilistic FT designs. An elegant and powerful method to construct covering graphs or CG's, which are key to obtaining the probabilistic FT designs, is to use linear error-correcting codes (ECCs). We show how to construct probabilistic designs with very high average fault tolerance but low wiring and switch overhead using ECCs like the 2D-parity, full-two, 3D-parity, and full-three codes. Given a graph G on n nodes the authors say that a graph T on n + k nodes is a k-fault tolerant version of G, if one can embed G in any n node induced subgraph of T. Thus T can sustain k faults and still emulate G without any performance degradation. They show that for a wide range of values of n, k and d, for any graph on n nodes with maximum degree d there is a k-fault tolerant graph with maximum degree O(kd). They provide lower bounds as well: there are graphs G with maximum degree d such that any k-fault tolerant version of them has maximum degree at least Omega (d square root k). >