Fast and efficient real-time route discovery via modified bidirectional A* algorithm

• Proposes MBiA*, a modified bidirectional A* for real-time route discovery on road graphs. • Introduces an incumbent-bound early-termination rule with proved optimality conditions. • Supports directed networks via direction-aware backward expansion for one-way constraints. • Provides theoretical analysis: correctness, termination, and worst-case complexity bounds. • Validates on time-sliced traffic snapshots with repeated-run timing statistics and CIs. Urban mobility applications increasingly r