Oriented Street Segments for Complete Building Addressing: A Graph-Theoretic Formulation, a Street-Side Choice Model and Error Propagation, Applied to Gombe (Kinshasa)

Our earlier work generated quality-scored addresses for ten cities from street graphs and supervised classifiers. Here we restate that pipeline mathematically and apply it, completely, to one commune: Gombe, the administrative centre of Kinshasa (Democratic Republic of the Congo; km2, buildings from OpenStreetMap and Google Open Buildings, addresses already in use). The street network is treated as an embedded planar graph whose oriented segments (darts, half-edges) carry the two sides of every street, and whose faces are the urban blocks. In this language we (i) prove that the published street-continuity score never joins straight continuations and give a corrected, name-aware matching; (ii) define an invertible oriented-segment address (S,σ,s,d) (street, side, position, offset) from which the human-readable address is rendered; (iii) formalise anchored house numbering (Theil–Sen fit, parity projection, order preservation and infill without renumbering) and block (îlot) addressing on faces; (iv) introduce a conditional-logit model over the candidate street sides of each building, with an optional Markov random field on the building adjacency graph; and (v) derive and simulate how input errors propagate through the graph. On Gombe, every building receives an address; anchored numbers are within ±10 of the number in use for % of test addresses (published model: %). The Euler relation holds exactly on the dart structure (|V|−|E|+|F|=2C=), and the nearest street lies on the building’s own face for % of buildings. The street-side choice model agrees with the street of existing addresses for % of them in leave-one-out validation, against % for the V8 rules and % for the nearest street; the Markov prior does not improve on it. Monte Carlo error experiments show that local errors stay local except through two global quantities, the betweenness ranks of provisional street codes and the commune numbering rate, which carry most of the propagated damage (% of the addresses changed by a missing segment are re-ranked codes). Both should therefore be frozen once addresses are issued.