1. Consider the 3x3 mesh. Find a set of latencies and a TTL value for which short circuiting effects occur. Quantify how large is the effect? That is, you should determine how much horizon reduction can occur in this network for each of the following cases
a) the latencies are symmetric (same in both directions)
b) the latencies are asymmetric (not necessarily same in both directions)
c) the are up to four additional edges added to the mesh.
2. In the proof of Theorem 3 of the paper "Latency Effects..." it states that for any submodular set function, the k-Greedy covering algorithm yields a good approximation ratio. Show that the t-Horizon function is not submodular.
3. In the notes on Hashing the authors suggest using a "Universal Class of Hash Functions". Formally define this term. Find a universal class of hash functions that would be appropriate for the application we have discussed. Discuss why the function is appropriate for the application.
4. Submit final project topic description. You can choose a paper from the literature to present or a larger-scale project. Here is listing of possible topic research papers.