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- W2345496427 abstract "In this paper, we study a set of combinatorial optimization problems on weighted graphs: the shortest path problem with negative weights, the weighted perfect bipartite matching problem, the unit-capacity minimum-cost maximum flow problem and the weighted perfect bipartite $b$-matching problem under the assumption that $Vert bVert_1=O(m)$. We show that each one of these four problems can be solved in $tilde{O}(m^{10/7}log W)$ time, where $W$ is the absolute maximum weight of an edge in the graph, which gives the first in over 25 years polynomial improvement in their sparse-graph time complexity. At a high level, our algorithms build on the interior-point method-based framework developed by Madry (FOCS 2013) for solving unit-capacity maximum flow problem. We develop a refined way to analyze this framework, as well as provide new variants of the underlying preconditioning and perturbation techniques. Consequently, we are able to extend the whole interior-point method-based approach to make it applicable in the weighted graph regime." @default.
- W2345496427 created "2016-06-24" @default.
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- W2345496427 date "2016-05-05" @default.
- W2345496427 modified "2023-10-17" @default.
- W2345496427 title "Negative-Weight Shortest Paths and Unit Capacity Minimum Cost Flow in Õ(m 10/7 log W) Time." @default.
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