FGA's Graph Algorithms Course Blog

  (Quiz week 12, nov 17th )  About fundamental definitions and hypotheses of communities, which of the statements below is false: A network's community structure is uniquely encoded in its wiring diagram. A network corresponds to a connected subgraph. Communities correspond to locally dense neighborhoods of a network. A clique is a subgraph of k-nodes. None of the above Original idea by: Fábio Assunção.

  (Quiz week 11, nov 10th )  The 3 layouts bellow show the distribution of 5 containers with inflamable substance distributed on a chemical floor. So, it's important trying to find the most safe distribution of the containers in order to prevent a catastrofical event on which a container explode and the explosion propagates to other(s) container(s) nearby. To analyse an eventual cascading failure through the networks represented by the containers distributions, consider the Failure Propagation Model. Also, consider breakdown treshold $\varphi = 0.4$ for all nodes.                                         Distribution 1 Distribution 2 Distribution 3 For each distribution, consider the 5 scenarios, where a failure initiates at node A, B, C, D and E, respectively. Is correct to state that : If initial failure occurs at node A, all 3 distributions propagates failures to neighbors nod...

  (Quiz week 10, nov 3rd )  The condition for running a DFS algorithm  on the network defined bellow  is by using alfabetical order. Then, by applying Kosaraju-Sharir's algorithm, the alternative that contains the correct trees corresponding to the SCC of the network is: BA, C, ED. A, CDE, B. BA, CED. AC, DE, B. None of the above Original idea by: Fábio Assunção.

>>>>>>>>>>>>>>>>> UNDER ELABORATION <<<<<<<<<<<<<<<<<<   (Quiz week 10, oct 20th )  elaborating

(Quiz week 8, oct 6th )  Suppose you are building a Barabási-Albert Model network at time $t$. Then, at time $t+1$, you are adding a new node U, that will attach to node C, given C's probability 0.75. Knowing that, assest the networks 1, 2, 3 and 4, bellow: The network the meets the correct configuration at time $t$ to receive U at time $t+1$ is: 1. 2. 3. 4. None of the above Original idea by: Fábio Assunção.

(Quiz week 7, sep 29th )  Consider $f''$ and $g$ defined as follows: $f''(x) = x^{-(1/3)}$ $g = 4x^5 + 2x^3 + 5 + 3x$ Then, considering derivation, which option bellow is correct: $f'''(x) = -(1/3)x^{-(3/4)}$ and $g'(x) = 20x^4 + 6x - 3$ $f'''(x) = -(1/3)x^{-(3/2)}$ and $g'(x) = 20x^4 + 6x^2 - 3$ $f'(x) = (3/2)x^{2/3}+6$ and $g'(x) = 4x^4 + 2x^2 - 3$ $f'(x) = (3/2)x^{2/3}+3$ and $g'(x) = 20x^4 + 6x^2 - x$ None of the above Original idea by: Fábio Assunção.