Constraint-Efficient Routing via Dual Graph on Road Name Address Hierarchy

Routing under real-world constraints such as turn restrictions, time-of-day rules, and vehicle-class conditions causes node proliferation in Primal Graph representations: each constrained intersection must be split into multiple via-nodes, inflating the graph super linearly with constraint count. This paper proposes a Dual Graph formulation built natively on the three-tier road name address hierarchy of the Korean Road Name Address system—daero (boulevard), ro (road), and gil (lane)—in which named roads are nodes and inter-road intersections are edges. Because constraints are encoded as edge attributes rather than node splits, the node count |VD| is invariant under any number of additional constraints. 

The graph is constructed entirely from the Basic Section Index (bsi), the coordinate-free linear measure established in [1], without geocoding or spatial computation. Two intersection tables derived from 369,597 national road records form the edge set: road_conn (79,760 Type I edges among ro/daero pairs) and intrsct_index (205,433 Type II edges connecting gil roads to intersecting ro/daero roads).

We prove that the Dual node count is O(1) with respect to constraint count while the Primal equivalent grows as O(¯dk), where ¯dis mean intersection degree and k is the number of applied constraint types. Empirical validation on Seoul (25 districts, 13,633 road nodes, 3,378 Type I edges) shows that at a 20% turn-restriction rate, Primal node count reaches 25,243 for Gangnam-gu while the Dual count remains fixed at 876.

Dijkstra on the Dual Graph achieves sub-millisecond intra-district latency (p50=0.90ms, p95=1.58ms for Gangnam-gu, 876 nodes). For cross-district routing across all 25 Seoul districts, a hierarchical scheme combining pre-computed intra-district shortcuts (sig_paths) with boundary edges (sig_exit) yields p50=3.84ms, a 5.3× improvement over flat single graph Dijkstra (p50=20.41ms)