A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Polynomial time algorithms for some evacuation problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
The Quickest Transshipment Problem
Mathematics of Operations Research
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
A fully combinatorial algorithm for submodular function minimization
Journal of Combinatorial Theory Series B
Faster Algorithms for the Quickest Transshipment Problem
SIAM Journal on Optimization
The Quickest Multicommodity Flow Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Discrete Applied Mathematics - Submodularity
Solving Evacuation Problems Efficiently--Earliest Arrival Flows with Multiple Sources
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
SIAM Journal on Computing
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
Evacuation of rectilinear polygons
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Approximating earliest arrival flows in arbitrary networks
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Earliest arrival flows in networks with multiple sinks
Discrete Applied Mathematics
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Earliest arrival flows capture the essence of evacuation planning. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink “as quickly as possible.” The latter requirement is made more precise by the earliest arrival property, which requires that the total amount of flow that has arrived at the sink is maximal for all points in time simultaneously. It is a classical result from the 1970s that, for the special case of a single source node, earliest arrival flows do exist and can be computed by essentially applying the successive shortest-path algorithm for min-cost flow computations. Although it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open for many years. We present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem.