Solving Flow Problems using Multiplicative Weights
نویسندگان
چکیده
We saw that using the multiplicative weights (MW) algorithm, we find a (1 + ε)-approximate max flow f̂—i.e., a flow of value F that has f̂e ≤ 1 + ε—using O( logm ε2 ) calls to the oracle. In Lecture #14, we saw that using shortest-path routing, you can get ρ = F . Since we can use Dijkstra’s O(m+ n log n) to implement the oracle, this gives an Õ( ε2 ) time algorithm. Relaxed Oracle: For the rest of this section, we are going to relax the requirements for the oracle, so that we merely want the flow to satisfy the capacity constraints approximately: ∑
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