CSC303: Practice Questions II
Rise of the New Practice Set
We¡¯ll be covering solutions in-tutorial on March 17th
Question 1: Recall the product diffusion process described in class. Recall that each node using product A has a reward of a per neighbour also using A, and that each node using product B has a reward of b per neighbour also using B.
Assume that we change our model so that mismatching neighbours each get a reward of c < a, b. For a node u using B, what proportion of u¡¯s neighbours must be using A for it to be non-detrimental for u to switch?
Question 2: In class we saw how to represent SIS using SIR. In tutorial you will be seeing the SEIR model. In the SEIR model, when a node is infected, is spends tE timesteps in a non-infectious ¡°exposed¡± state before transitioning to the infectious state.
How can you represent SEIR as a SIR model with tE = 1? Assume the SEIR contact network is directed.
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Question 3: Consider the problem of decentralized search. Assume that instead of only providing a node with it¡¯s neighbours and their grid-distance to the target, we also provide a node with their neighbours¡¯ weak links. How could you improve the decentralized search heuristic with this information?
Question 4: Assume you run a fast food restaurant. The sales of your products roughly follow a power law distribution. To take advantage of bulk purchases, you would like to maximize the inequality in the sales distribution. How could you do this?
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Question 5: Compute the structural virality of a graph consisting of a node u0 with n children, u1, . . . un.
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Question 6: Describe a graph which is not a social network (i.e., the nodes cannot be people or similarly intelligent entities such as companies), but where triadic closure could be argued to be applicable.