This question is basically five questions stapled together and they want you to hold all of it in your head simultaneously.
Start by formalizing the objective function that balances passenger wait time and deadhead miles, then describe a streaming assignment system that handles uncertainty via probabilistic ETA distributions. Walk through the data structures, algorithmic approach, and how you update assignments as new information arrives, while addressing fairness, complexity, and fallback strategies.
Pro tip: Emphasize the trade-off between optimality and real-time constraints: use a rolling horizon with approximate algorithms (e.g., greedy with lookahead) and quantify the competitive ratio under worst-case scenarios to show rigor.
Formalize the objective as a weighted sum of expected passenger wait time and deadhead miles, subject to driver availability, vehicle capacity, and fairness constraints. Discuss how to incorporate Gaussian ETA uncertainty (e.g., using expected values or chance constraints).
Propose data structures for efficient nearest-neighbor queries (e.g., KD-trees, geohashes) and priority queues for pending requests. Describe a streaming pipeline that ingests flight ETA updates and driver locations, triggering reassignment when significant changes occur.
Outline a rolling-horizon assignment algorithm: at each time step, solve a bipartite matching problem (e.g., Hungarian algorithm) on a subset of drivers and requests, using expected wait and deadhead costs. For scalability, consider greedy or auction-based approximations.
Explain how to update assignments when flight ETAs change (e.g., re-optimize affected matches) and handle cancellations by freeing drivers. Incorporate fairness via constraints like max wait time per driver or rotating priority.
Provide complexity analysis (e.g., O(n^3) for Hungarian, O(n log n) for greedy) and discuss competitive ratio or worst-case bounds. Propose fallback strategies for demand spikes, such as surge pricing, driver rebalancing, or relaxed fairness constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.