by Luis Eduardo Muñoz Guerrero
ABSTRACT
To measure how close the lighthouse networks of England and Wales (1693–1911) and France (1775–1929) came to optimal siting, and whether the centrally planned French programme of 1825 sited lights better than incremental English provision. Siting was formulated as a maximum coverage location problem over a 20 km sea band, solved exactly by integer programming and approximately by a lazy greedy algorithm with a (1−1/e) guarantee and certified bounds, on two public datasets (603 and 1,139 light records) in a reproducible pipeline with perturbation replicates and 15 alternative specifications. With a common range of 18.5 km, networks too small to cover the band reached 0.50–0.77 of the optimum. English siting in 1693 was no better than random, and French waves before 1825 were near random (normalised efficiency 0.01 and 0.05); programme waves reached 0.53–0.55 with observed ranges, against 0.38 in England and Wales, a small, specification-dependent margin under a common range. At every benchmark, greedy solutions stayed within 1.1% of exact optima; common-range optima took at most 0.249 s. Conclusions: Under the French programme, construction moved from near random to closing about half the gap to optimal siting with observed ranges; exact benchmarks can audit infrastructure heritage.
