Ingrid Barbosa

For each statement below, indicate whether it is True or False. I) The traveling salesperson problem seeks a cycle that visits every vertex exactly once and has the minimum possible total weight. II) In the symmetric TSP, the closest neighbor heuristic always guarantees an optimal solution. III) The triangle inequality states that for any three nodes x, y, and z, the direct cost from x to y cannot exceed the cost of traveling through z. IV) TSP is considered NP-Hard; therefore, if a polynomial-time algorithm for TSP were discovered, every problem in NP could also be solved in polynomial time. a) I, II, III and IV are correct b) Only I and IV are correct c) II and IV are correct d) I, III and IV are correct e) None of the above Original idea by Ingrid Barbosa

A malware strain is released into a computer network with 10,000 devices, modeled as a scale-free graph with γ = 2.5 and ⟨k⟩ = 4. The malware spreads via the SIS model with infection rate β = 0.3 and recovery rate μ = 0.15. The initial attack targets a single randomly chosen node. What is the basic reproductive number R₀, and what does it imply for the cyberattack? a) R₀ = 0.5 and the attack will die out exponentially. b) R₀ = 2.0 and the attack is above threshold and can produce a large-scale epidemic. c) R₀ = 1.0 and the network is at the critical point and spreading is unpredictable. d) R₀ = 8.0 and only hubs can sustain the infection. e) None of the above. Original idea by Ingrid Barbosa