In the problem of reliable multiparty computation (RC), there are @math parties, each with an individual input, and the parties want to jointly compute a function @math over @math inputs. The problem is complicated by the fact that an omniscient adversary controls a hidden fraction of the parties. We describe a self-healing algorithm for this problem. In particular, for a fixed function @math , with @math parties and @math gates, we describe how to perform RC repeatedly as the inputs to @math change. Our algorithm maintains the following properties, even when an adversary controls up to @math parties, for any constant @math . First, our algorithm performs each reliable computation with the following amortized resource costs: @math messages, @math computational operations, and @math latency, where @math is the depth of the circuit that computes @math . Second, the expected total number of corruptions is @math , after which the adversarially controlled parties are effectively quarantined so that they cause no more corruptions.
With the employment of very high capacity transmission systems in high-speed broadband networks (B-ISDN, broadband integrated services digital network), based upon the asynchronous transfer mode (ATM), the consequences of a link failure have increased, since even during a short disconnection a large volume of data is lost. These networks can be made safer against failure, if in the case of a transmission link outage the affected traffic is routed over still intact network parts. This paper describes various protection switching methods for ATM networks and presents mathematical models which can be used to determine globally optimal restoration paths and to dimension spare capacities in the network. Finally, the results are discussed and the various methods are compared. In self-healing networks, end-to-end restoration schemes have been considered more advantageous than line restoration schemes because of a possible cost reduction of the total capacity to construct a fully restorable network. This paper clarifies the benefit of end-to-end restoration schemes quantitatively through a comparative analysis of the minimum link capacity installation cost. A jointly optimal capacity and flow assignment algorithm is developed for the self-healing ATM networks based on end-to-end and line restoration. Several networks with diverse topological characteristics as well as multiple projected traffic demand patterns are employed in the experiments to see the effect of various network parameters. The results indicate that the network topology has a significant impact on the required resource installation cost for each restoration scheme. Contrary to a wide belief in the economic advantage of the end-to-end restoration scheme, this study reveals that the attainable gain could be marginal for a well-connected and or unbalanced network. This paper studies the capacity and flow assignment problem arising in the design of self-healing asynchronous transfer mode (ATM) networks using the virtual path concept. The problem is formulated here as a linear programming problem which is solved using standard methods. The objective is to minimize the spare capacity cost for the given restoration requirement. The spare cost depends on the restoration strategies used in the network. We compare several restoration strategies quantitatively in terms of spare cost, notably: global versus failure-oriented reconfiguration, path versus link restoration, and state-dependent versus state-independent restoration. The advantages and disadvantages of various restoration strategies are also highlighted. Such comparisons provide useful guidance for real network design. Further, a new heuristic algorithm based on the minimum cost route concept is developed for the design of large self-healing ATM networks using path restoration. Numerical results illustrate that the heuristic algorithm is efficient and gives near-optimal solutions for the spare capacity allocation and flow assignment for tested examples. The total transmission capacity required by a transport network to satisfy demand and protect it from failures contributes significantly to its cost, especially in long-haul networks. Previously, the spare capacity of a network with a given set of working span sizes has been optimized to facilitate span restoration. Path restorable networks can, however, be even more efficient by defining the restoration problem from an end to end rerouting viewpoint. We provide a method for capacity optimization of path restorable networks which is applicable to both synchronous transfer mode (STM) and asynchronous transfer mode (ATM) virtual path (VP)-based restoration. Lower bounds on spare capacity requirements in span and path restorable networks are first compared, followed by an integer program formulation based on flow constraints which solves the spare and or working capacity placement problem in either span or path restorable networks. The benefits of path and span restoration, and of jointly optimizing working path routing and spare capacity placement, are then analyzed. For restoration in the case of single link failures in meshed networks several strategies can be considered: link restoration, path restoration and path restoration with link-disjunct route. In terms of spare capacity requirement path restoration is found to be most attractive. These results are obtained by using two general optimisation techniques (simulated annealing and integer linear programming). Both techniques have each their own features; their applicability depends on the size and type of the problem. Application to WDM fibre networks is discussed.