Graphs and algorithms
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
A survey of dynamic network flows
Annals of Operations Research
Combinatorial algorithms for the generalized circulation problem
Mathematics of Operations Research
A faster deterministic maximum flow algorithm
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A faster combinatorial algorithm for the generalized circulation problem
Mathematics of Operations Research
Polynomial-time highest-gain augmenting path algorithms for the generalized circulation problem
Mathematics of Operations Research
Faster Algorithms for the Generalized Network Flow Problem
Mathematics of Operations Research
Polynomial time algorithms for some evacuation problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Minimum cost flows over time without intermediate storage
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow
Mathematics of Operations Research
Generalized maximum flow algorithms
Generalized maximum flow algorithms
Improving time bounds on maximum generalised flow computations by contracting the network
Theoretical Computer Science - Special issue on automata, languages and programming
SIAM Journal on Computing
A simple GAP-canceling algorithm for the generalized maximum flow problem
Mathematical Programming: Series A and B
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
Approximating earliest arrival flows in arbitrary networks
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Flows over time and generalized flows are two advanced network flow models of utmost importance, as they incorporate two crucial features occurring in numerous real-life networks. Flows over time feature time as a problem dimension and allow to realistically model the fact that commodities (goods, information, etc.) are routed through a network over time. Generalized flows allow for gain/loss factors on the arcs that model physical transformations of a commodity due to leakage, evaporation, breeding, theft, or interest rates. Although the latter effects are usually time-bound, generalized flow models featuring a temporal dimension have never been studied in the literature. In this paper we introduce the problem of computing a generalized maximum flow over time in networks with both gain factors and transit times on the arcs. While generalized maximum flows and maximum flows over time can be computed efficiently, our combined problem turns out to be NP-hard and even completely non-approximable. A natural special case is given by lossy networks where the loss rate per time unit is identical on all arcs. For this case we present a (practically efficient) FPTAS.