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2015

Flow Rounding

Kang, Donggu, Payor, James

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Understand

We consider flow rounding: finding an integral flow from a fractional flow.

Costed flow rounding asks that we find an integral flow with no worse cost.
Randomized flow rounding requires we randomly find an integral flow such that the expected flow along each edge matches the fractional flow.
Both problems are reduced to cycle canceling, for which we develop an $O(m \log(n^2/m))$ algorithm.

Flow Rounding · Around

Built on

A data structure for dynamic trees
Sleator, D. D. and Tarjan, R. E. (1981) · 1981
Earlier work this paper cites.
Provably good routing in graphs: regular arrays
Raghavan, P. and Thompson, C. D. (1985) · 1985
Earlier work this paper cites.
Randomized rounding: A technique for provably good algorithms and algorithmic proofs
Raghavan, P. and Tompson, C. D. (1987) · 1987
Earlier work this paper cites.

Similar

Finding minimum-cost circulations by canceling negative cycles
Goldberg, A. V. and Tarjan, R. E. (1989) · 1989
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Approximate max-flow on small
Cohen, E. (1995) · 1995
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Optimal Rounding of Instantaneous Fractional Flows Over Time
Fleischer, L. K. and Orlin, J. B. (2000) · 2000
Cited alongside, same era.

Then

A New Approach to Computing Maximum Flows using Electrical Flows
Lee, Y. T., Rao, S., and Srivastava, N. (2013) · 2013
Later among the works it cites.
Navigating central path with electrical flows: From flows to Matchings, and back
Madry, A. (2013) · 2013
Later among the works it cites.

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