A polynomial combinatorial algorithm for generalized minimum cost flow
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Faster approximation algorithms for generalized flow
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improving time bounds on maximum generalised flow computations by contracting the network
Theoretical Computer Science - Special issue on automata, languages and programming
A simple GAP-canceling algorithm for the generalized maximum flow problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
Theoretical Computer Science
Faster approximate lossy generalized flow via interior point algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A faster combinatorial approximation algorithm for scheduling unrelated parallel machines
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Generalized maximum flows over time
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
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We consider the generalized network flow problem. Each arc e in the network has a gain factor γ(e). If f(e) units of flow enter arc e, then f(e)γ(e) units arrive at the other end of e. The objective is to maximize the net flow into one specific node, the sink. The constraints are the conservation of flow at nodes and the capacities of arcs. We present a combinatorial algorithm which solves this problem in O(m2(m + n log log B)log B) time, where n is the number of nodes, m is the number of arcs, and B is the largest integer used to represent the gain factors, the capacities, and the initial supplies at the nodes. If m is O(n4/3 - ε) and B is not extremely large, then our bound is better than the previous best upper bound for this problem. We also improve the best known upper bound for the approximate generalized flow problem by showing that a solution whose value is within a factor of 1 + ξ from the optimum can be computed in O(m(m + n log log B) log(1/ξ)) time plus O(mn2 log B) time for preprocessing.