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We develop the first polynomial combinatorial algorithm for generalized minimum cost flow. Despite a rich history dating back to Kantorovich and Dantzig, until now, the only known way to solve the problem in polynomial-time was via ellipsoid or interior point methods Flow-based polynomial algorithms were previously known only for the version of our problem… (More)

- Kevin Daniel Wayne, Jon Lee, Jim Renegar, Sid Resnick, David Shmoys, Eva Tardos +5 others
- 1998

We present several new efficient algorithms for the generalized maximum flow problem. In the traditional maximum flow problem, there is a capacitated network and the goal is to send as much of a single commodity as possible between two distinguished nodes, without exceeding the arc capacity limits. The problem has hundreds of applications including:… (More)

We present fast and simple fully polynomial time approximation schemes (FPTAS) for generalized versions of maximum ow, multicommodity ow, minimum cost ow, and minimum cost multicommodity ow. Our FPTAS's dominate the previous best known complexity bounds for all of these problems, some by more than a factor of n 2. Our generalized multicommodity FPTAS's are… (More)

We i n troduce a gain-scaling technique for the generalized maximum ow problem. Using this technique, we present three simple and intuitive polynomial-time combinatorial algorithms for the problem. Truemper's augmenting path algorithm is one of the simplest combi-natorial algorithms for the problem, but runs in exponential-time. Our rst algorithm is a… (More)

We present faster FPTAS's for generalized versions of the maximum flow, multicommodity flow, minimum cost flow, and miniium cost multicommodity flow problems in lossy networks. We dominate the previous best known complexity bounds for all of these problems, some by as much as a factor of n2. Our generalized multicommodity FPTAS's are now as fast as the best… (More)

In the baseball elimination problem, there is a league consisting of n teams. At some point during the season, team i has wi wins and gij games left to play against team j. A team is eliminated if it cannot possibly finish the season in first place or tied for first place. The goal is to determine exactly which teams are eliminated. The problem is not as… (More)

- Kevin Wayne
- 2015

Divide-and-conquer.

- Chun Wa Ko, Jon Lee, Kevin Wayne
- 1998

We i n troduce a spectral bound for D-optimal design problems , based on singular values. We compare the spectral bound to a bound based on Hadamard's inequality which w as introduced by W elch. In particular , we demonstrate that i in general, neither bound dominates the other, ii the spectral bound is superior in a general situation of highly replicated… (More)

- Kevin Wayne
- 2013

• max-flow and min-cut problems • Ford-Fulkerson algorithm • max-flow min-cut theorem • capacity-scaling algorithm • shortest augmenting paths • blocking-flow algorithm • unit-capacity simple networks • max-flow and min-cut problems • Ford-Fulkerson algorithm • max-flow min-cut theorem • capacity-scaling algorithm • shortest augmenting paths • blocking-flow… (More)

- Mark Colhoun, Rainer Dahlenburg, Ms Mary, E Ziggie Greene, Mr Malyniwsky, Meshack Pabalala +10 others
- 2011

Symbols of United Nations documents are composed of letters combined with figures. Mention of such symbols indicates a reference to a United Nations document. The designations employed and the presentation of material in this publication do not imply the expression of any opinion whatsoever on the part of the Secretariat of the United Nations concerning the… (More)