SQL Query Optimizer

Optimize the following SQL query for better performance:

```sql
[YOUR SQL QUERY]
```

Database: [MySQL/PostgreSQL/SQLite/etc.]
Table sizes: [approximate row counts]
Current execution time: [if known]

Please:
1. Identify performance bottlenecks
2. Suggest appropriate indexes
3. Rewrite the optimized query
4. Explain each optimization
5. Show EXPLAIN output analysis
6. Consider edge cases