This is just the Travelling Salesman Problem with a thin coat of drone paint on it.
Recognize this as the Asymmetric Traveling Salesman Problem (ATSP) and propose a solution using dynamic programming with bitmasking (Held-Karp algorithm) for exact results on small inputs, or a heuristic like nearest neighbor with 2-opt for larger inputs. Discuss the time and space complexity trade-offs and justify your choice based on the expected number of hubs.
Pro tip: Mention that for asymmetric costs, you cannot assume the triangle inequality, so heuristics like nearest neighbor may perform poorly; consider using the Held-Karp algorithm for exactness or Christofides-like adaptations for approximation. Also, clarify with the interviewer whether the number of hubs is small enough for exponential algorithms or if a heuristic is acceptable.
Confirm that the drone must visit each hub exactly once and return to the start, and that the cost matrix is asymmetric. Ask about the expected number of hubs to determine if an exact or heuristic approach is needed.
State that this is the Asymmetric Traveling Salesman Problem (ATSP), which is NP-hard. Explain that for small N, exact algorithms like Held-Karp (DP with bitmasking) are feasible, while for large N, heuristics are necessary.
Describe the Held-Karp algorithm: use DP where state is (current hub, set of visited hubs) and value is minimum cost to reach that state from start. Recurrence: dp[S][i] = min over j in S\{i} of dp[S\{i}][j] + cost[j][i]. Base case: dp[{0}][0] = 0. Answer: min over i of dp[all][i] + cost[i][0].
Analyze time complexity O(N^2 * 2^N) and space O(N * 2^N). Mention that this is exponential and only suitable for N up to ~20. For larger N, suggest heuristics like nearest neighbor, 2-opt, or genetic algorithms, and note that they may not find the optimal solution.
Mention possible optimizations: pruning, memoization, or using branch-and-bound. Also, note that if the cost matrix has special structure (e.g., satisfies triangle inequality), other algorithms might apply, but asymmetry complicates things.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.