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Abif Arad algorithm analysis angle anisotropic arcs area served assume assumption BECKMANN branch compute configuration conformal mapping consider constant density construction cost cos(y cost of transport cost parameters curvature curve decreasing denote density q depend derived detour factor direct transport discrete disk distance Euclidean distance Figure flow freight function given hence hexagons holds isotropic LAUNHARDT Law of Junction length location theory logarithmic spirals minimum network location network problem network radials networks of radial number of radials optimal network optimal transport optimally located optimum number polar coordinates population density r q dr r q(r R-pattern radial lines radius regular polygon routing Section IV.2 sector simple bifurcation siny site x solution source density STEINER point STEINER problem straight line straight network lines surface lines Theorem tion total cost traffic transfer cost transport divides transport line transportation area transportation network Transportation Sci tt/y urban vertex vertices VORONOI diagrams yields