Scaling algorithms for network problems
Journal of Computer and System Sciences
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
An O(n2 log n) parallel max-flow algorithm
Journal of Algorithms
A parallel algorithm for finding a blocking flow in an acyclic network
Information Processing Letters
A parallel blocking flow algorithm for acyclic networks
Journal of Algorithms
A faster deterministic maximum flow algorithm
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
On the power of segmenting and fusing buses
Journal of Parallel and Distributed Computing
Constant time graph algorithms on the reconfigurable multiple bus machine
Journal of Parallel and Distributed Computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Parallel Real-Time Computation: Sometimes Quantity Means Quality
ISPAN '00 Proceedings of the 2000 International Symposium on Parallel Architectures, Algorithms and Networks
Computing nearest neighbors in real time
Journal of Parallel and Distributed Computing
On the importance of parallelism for quantum computation and the concept of a universal computer
UC'05 Proceedings of the 4th international conference on Unconventional Computation
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The dynamic version of the maximum flow problem allows the graph underlying the flow network to change over time. The graph receives corrections to its structure or capacities and consequently the value of the maximum flow is modified. Several correction types are treated: edge capacity corrections and constant degree vertex additions/deletions. These corrections arrive in real time. In this paper, parallel and sequential solutions to the real-time maximum flow problem are developed on the reconfigurable multiple bus machine model and on the random access machine model, respectively. The parallel solution successfully meets the deadlines imposed in real time, while the sequential one fails to do so.The two solutions are then applied to a real-time process scheduler, an extension of Stone's static two-processor allocation problem. The scheduler allows processes to be created and destroyed, the amount of communication between two processes to change with time, and so on. The parallel algorithm is always able to compute the optimal schedule, while the solution obtained sequentially is only an approximation. The sequential solution gets worse with each new deadline to be met. In fact, after a sufficient number of steps, the quality improvement provided by the parallel approach over the sequential one is superlinear in the number of processors used by the parallel model.