Distributed function evaluation in the presence transmission faults
SIGAL '90 Proceedings of the international symposium on Algorithms
Broadcasting in a hypercube when some calls fail
Information Processing Letters
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Broadcasting in hypercubes and star graphs with dynamic faults
Information Processing Letters
Optimal broadcasting in hypercubes with dynamic faults
Information Processing Letters
On fractional dynamic faults with thresholds
Theoretical Computer Science
Deterministic Models of Communication Faults
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Rapid almost-complete broadcasting in faulty networks
Theoretical Computer Science
Rapid almost-complete broadcasting in faulty networks
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Consensus vs. broadcast in communication networks with arbitrary mobile omission faults
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
On fractional dynamic faults with threshold
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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We consider a broadcasting problem in the n-dimensional hypercube 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. Given a number m ≤ n - 1, the problem is to determine the minimum broadcasting time if at most m faults are allowed in any step. The case m = n - 1 was studied in Chlebus et al. (Networks 27 (1996) 309), De Marco and Vaccaro (Inform. Process. Lett. 66 (1998) 321), Fraigniaud and Lazard (Inform. Process. Lett. 39 (1991) 115) and completely solved in Dobrev and Vrto (Inform. Process. Lett. 71 (1999) 81). A related problem, what is the maximal m s.t. the minimum broadcasting time remains n was proposed in De Marco and Vaccaro (Inform. Process. Lett. 66 (1998) 321). We prove that for m ≤ n - 3 the minimum broadcasting time is n. If m = n - 2 the broadcasting time is always at most n + 1, for n 3, and the upper bound is the best possible. Our method is related to the isoperimetric problem in graphs and can be applied to other networks.