Ingrid Barbosa

The Unicamp Campus administration plans to create paths connecting all restaurants to optimize pedestrian mobility. Due to environmental restrictions, it's not allowed to build tunnels, and no path can cross another. Considering the Unicamp's map below, where the red dots represent the restaurants, analyze the statements: a) The project is feasible, since it is possible to create a path that connects all the 8 restaurants without crossing. b) The project would only be feasible if two of the restaurants were not directly connected to the others. c) The project would be feasible if the restaurants were divided into 2 groups of 4, and only one path would connect both groups. d) There is no way that the project would be feasible. e) None of the above. Original idea by: Ingrid Barbosa

A research data center needs to transfer data to a remote backup facility during a 4‑hour maintenance window. The data transfer process is modeled as a directed network, where nodes represent logical components (functional stages) of the data transfer pipeline, and edges represent logical communication channels, with limited capacity. In this model, node A represents the point where data is generated in the primary data center. The intermediate nodes (B, C, D) represent functional stages of the transfer process, such as internal processing, aggregation, or interfaces to external networks. And the node E represents the logical destination where data is finally stored at the backup site. All edges have constant transmission capacity, except for one critical link, whose capacity varies over time due to shared usage with other services. The network is described as follows, with capacities measured in GB/hour: \( A→B: Capacity = 8 \) \( B→C: Capacity = 4 + 2sin(\frac{πt}{4}) \) \( C...