i need help in these two problems and i need them solved by TWO different ways (the 1st problem in two ways and also the 2nd problem in two different ways) but they should be correct these are the problems: 1. Carry out a proof of a lower bound on time of oblivious routing protocols for the multi-port model using the approach for the single-port model, that is, working with node congestion. Hint: You are asked to prove any reasonable bound, as long as it is both correct and is obtained by way of working with node congestion. If you follow the proof for the single-port model closely enough, the obtained lower bound is pn=d3. 2. Propose a family of acyclic directed networks Gn, where Gn is of size n, and a strategy of the adversary of injection rate 1 that makes the size of queues at nodes of Gn as large as you can. Give an estimate of the resulting maximum size of queues at the nodes of Gn, in the form of a lower bound, as a function of n.
1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done.
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