In a (randomized) oblivious routing scheme the path chosen for a request between a source s and a target t is independent from the current traffic in the network. Hence, such a scheme consists of probability distributions over s − t paths for every source-target pair s, t in the network.In a recent result [11] it was shown that for any undirected network there is an oblivious routing scheme that achieves a polylogarithmic competitive ratio with respect to congestion. Subsequently, Azar et al.[4] gave a polynomial time algorithm that for a given network constructs the best oblivious routing scheme, i.e. the scheme that guarantees the best possible competitive ratio. Unfortunately, the latter result is based on the Ellipsoid algorithm; hence it is unpractical for large networks.In this paper we present a combinatorial algorithm for constructing an oblivious routing scheme that guarantees a competitive ratio of O(log 4 n) for undirected networks. Furthermore, our approach yields a proof for the existence of an oblivious routing scheme with competitive ratio O(log 3 n), which is much simpler than the original proof from [11].
The paper presents our actual knowledge and experience in joining dissimilar materials with the use of friction welding method. The joints of aluminium and aluminium alloys with the different types of steel were studied. The structural effects occurring during the welding process were described. The mechanical properties using, for example, (i) microhardness measurements, (ii) tensile tests, (iii) bending tests, and (iv) shearing tests were determined. In order to obtain high-quality joints the influence of different configurations of the process such as (i) changing the geometry of bonding surface, (ii) using the interlayer, or (iii) heat treatment was analyzed. Finally, the issues related to the selection of optimal parameters of friction welding process were also investigated.
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