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- W2726934493 abstract "Let R, B be a set of n points in R^d, for constant d, where the points of R have integer supplies, points of B have integer demands, and the sum of supply is equal to the sum of demand. Let d(.,.) be a suitable distance function such as the L_p distance. The transportation problem asks to find a map tau : R x B --> N such that sum_{b in B}tau(r,b) = supply(r), sum_{r in R}tau(r,b) = demand(b), and sum_{r in R, b in B} tau(r,b) d(r,b) is minimized. We present three new results for the transportation problem when d(.,.) is any L_p metric:* For any constant epsilon > 0, an O(n^{1+epsilon}) expected time randomized algorithm that returns a transportation map with expected cost O(log^2(1/epsilon)) times the optimal cost.* For any epsilon > 0, a (1+epsilon)-approximation in O(n^{3/2}epsilon^{-d}polylog(U)polylog(n)) time, where U is the maximum supply or demand of any point.* An exact strongly polynomial O(n^2 polylog n) time algorithm, for d = 2." @default.
- W2726934493 created "2017-07-14" @default.
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- W2726934493 date "2017-01-01" @default.
- W2726934493 modified "2023-09-24" @default.
- W2726934493 title "Faster Algorithms for the Geometric Transportation Problem" @default.
- W2726934493 doi "https://doi.org/10.4230/lipics.socg.2017.7" @default.
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