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Optimal Broadcasting in Tori with Dynamic Faults

We consider a broadcasting problem in the n-dimensional k-ary even torus in the shouting communication mode, i.e. any node of a network can inform all its neighbours in one time step. In addition, during any time step a number of links of the network can be faulty. Moreover the faults are dynamic. The problem is to determine the minimum broadcasting time if at most 2n - 1 faults are allowed in any step. In [4], it was shown that the broadcasting time is at most diameter+O(1), provided that k is limited by a polynomial of n. In our paper we drop this additional assumption and prove that the broadcasting can be always done in time diameter +2. The bound is the best possible.