Help Algorithms for Communication Networks 03

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.

## Deliverables

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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a)? For web sites or? other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment.

b) For all others including desktop software or software the buyer intends to distribute: A software? installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request.

3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement).

## Platform

NO coding

Evner: Lidt af Hvert

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Om arbejdsgiveren:
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Projekt ID: #3311933