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.
Our results are inspired by recent work on self-healing algorithms. Early work of @cite_7 @cite_13 @cite_21 @cite_25 @cite_2 discusses different restoration mechanisms to preserve network performance by adding capacity and rerouting traffic streams in the presence of node or link failures. This work presents mathematical models to determine global optimal restoration paths, and provides methods for capacity optimization of path-restorable networks.
@cite_7 @cite_21 @cite_2 @cite_13 @cite_25
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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. 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. Built upon a shared wireless medium, wireless network is particularly vulnerable to jamming attacks. The ability to recover from attacks and maintain an acceptable level of service degradation is a crucial aspect in the design of a wireless network. To address this issue, this paper investigates the network restoration solutions via the joint design of traffic rerouting, channel re-assignment, and scheduling. Efficient routing and channel assignment schemes can relieve the interference caused by both the normal network nodes and the jamming nodes. Therefore, based on the necessary conditions of schedulability, we first formulate the optimal network restoration problem as linear programming problem, which gives an upper bound on the achievable network throughput. After we solve the LP problems, we have a set of flows assigned to edges that have been assigned to different channels. And based on the LP solutions, we provide a greedy scheduling algorithm using dynamic channel assignment, which schedules both the network traffic and the jamming traffic. In particular, we consider two strategies, namely global restoration and local restoration, which can support a range of tradeoffs between the restoration latency and network throughput after restoration. To quantitatively evaluate the impact of jamming attacks during and after restoration, we define two performance degradation indices, transient disruption index (TDI) and throughput degradation index (THI). Finally, extensive performance evaluations are performed to study the impact of various jamming scenarios in a multi-hop multi-channel wireless network. 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.