Presents a successive shortest paths scaling algorithm for unit-capacity min-cost flow achieving Õ((nm)^{2/3} log C) time on planar multigraphs via r-divisions and dense distance graphs.
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A condensed time-expanded network with O(n²μ) nodes and O(μmn) edges solves max flow over time with μ capacity changes in O(μ²n³m) time.
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Min-Cost Flow in Unit-Capacity Planar Graphs
Presents a successive shortest paths scaling algorithm for unit-capacity min-cost flow achieving Õ((nm)^{2/3} log C) time on planar multigraphs via r-divisions and dense distance graphs.
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Brief announcement: A special case of maximum flow over time with network changes
A condensed time-expanded network with O(n²μ) nodes and O(μmn) edges solves max flow over time with μ capacity changes in O(μ²n³m) time.