Given an unweighted, undirected graph representing a social network, we need to find the shortest path between two users for every query. A standard BFS is too slow for real-time queries on a graph with 10 million nodes. Propose a two-level indexing or bidirectional search optimization strategy. Analyze the time and space complexity of your proposed solution compared to standard BFS, and explain the trade-offs involved in pre-processing versus query time.