This paper studies the problem of perfectly secure communication in general network in which processors and communication lines may be faulty. Lower bounds are obtained on the connectivity required for successful secure communication. Efficient algorithms are obtained that operate with this connectivity and rely on no complexity-theoretic assumptions. These are the first algorithms for secure communication in a general network to simultaneously achieve the three goals of perfect secrecy, perfect resiliency, and worst-case time linear in the diameter of the network.
In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point and multicast) where the goal is to route all requests while minimizing the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, A preliminary version of this paper appeared in it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, that is, for any on-line algorithm there exists a scenario in which ⍀(log n) increase in bandwidth is necessary in directed networks.We view virtual circuit routing as a generalization of an on-line load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases the machine's load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load.For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)-competitive algorithm. This stands in contrast to the natural greedy approach, whose competitive ratio is exactly n.
In this paper we study an idealized problem of on-line allocation of routes to virtual circuits where the goal is to minimize the required bandwidth. For the case where virtual circuits continue to exist forever, we describe an algorithm that achieves an O (log n) competitive ratio, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any on-line algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary.We view virtual circuit routing as a generalization of an on-line scheduling problem, and hence a major part of the paper focuses on development of algorithms for non-preemptive on-line scheduling for related and unrelated machines. Specialization of routing to scheduling leads us to concentrate on scheduling in the case where jobs must be assigned immediately upon arrival; assigning a job to a machine increases this machine's load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load.For the related machines case, we describe the first algorithm that achieves constant competitive ratio.For the unrekzted case (with n machines), we describe a new method that yields O(log n)-competitive algorithm. This stands in contrast to the natural greedy approach, which we show has only a~(n) competitive ratio. The virtual circuit routing result follows as a generalization of the unrelated machines case.
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