An algorithm for certain multi-commodity flow problems

Networks ◽  
1971 ◽  
Vol 1 (1) ◽  
pp. 75-90 ◽  
Author(s):  
Daniel J. Kleitman
Keyword(s):  
Commodity Flow ◽  
Flow Problems

scholarly journals Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1716
Author(s):  
Adrian Marius Deaconu ◽  
Delia Spridon
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Random Network ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Network Flow Problems ◽  
Commodity Flow ◽  
Vast Number ◽  
Flow Problems ◽  
Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

scholarly journals On solving multi-commodity flow problems: An experimental evaluation

2017 ◽  
Vol 30 (4) ◽  
pp. 1481-1492 ◽  
Author(s):  
Weibin DAI ◽  
Jun ZHANG ◽  
Xiaoqian SUN
Keyword(s):  
Experimental Evaluation ◽  
Commodity Flow ◽  
Flow Problems

A column generation and partitioning approach for multi-commodity flow problems

1994 ◽  
Vol 3 (3) ◽  
pp. 239-258 ◽  
Author(s):  
Cynthia Barnhart ◽  
Christopher A. Hane ◽  
Ellis L. Johnson ◽  
Gabriele Sigismondi
Keyword(s):  
Column Generation ◽  
Commodity Flow ◽  
Flow Problems

BINDING ALGORITHM FOR POWER OPTIMIZATION BASED ON NETWORK FLOW METHOD

2002 ◽  
Vol 11 (03) ◽  
pp. 259-271 ◽  
Author(s):  
YOONSEO CHOI ◽  
TAEWHAN KIM
Keyword(s):  
Network Flow ◽  
Power Optimization ◽  
Flow Problem ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Data Flow Graph ◽  
Commodity Flow ◽  
Behavioral Synthesis ◽  
Flow Problems ◽  
Step Procedure

We propose an efficient binding algorithm for power optimization in behavioral synthesis. In prior work, it has been shown that several binding problems for low-power can be formulated as multi-commodity flow problems (due to an iterative execution of data flow graph) and be solved optimally. However, since the multi-commodity flow problem is NP-hard, the application is limited to a class of small sized problems. To overcome the limitation, we address the problem of how we can effectively make use of the property of efficient flow computations in a network so that it is extensively applicable to practical designs while producing close-to-optimal results. To this end, we propose a two-step procedure, which (1) determines a feasible binding solution by partially utilizing the computation steps for finding a maximum flow of minimum cost in a network and then (2) refines it iteratively. Experiments with a set of benchmark examples show that the proposed algorithm saves the run time significantly while maintaining close-to-optimal bindings in most practical designs.

scholarly journals Approximate Algorithms for Continuous-Time Quickest Multi-Commodity Contraflow Problem

2020 ◽  
Vol 37 (1-2) ◽  
pp. 30-46
Author(s):  
Shiva Prakash Gupta ◽  
Durga Prasad Khanal ◽  
Urmila Pyakurel ◽  
Tanka Nath Dhamala
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Continuous Time ◽  
Flow Problem ◽  
Capacity Constraints ◽  
Approximate Algorithms ◽  
Optimal Solutions ◽  
Commodity Flow ◽  
Flow Problems

Multi-commodity flow problem appears when several distinct commodities are shipped from supply nodes to the demand nodes through a network without violating the capacity constraints. The quickest multi-commodity flow problem deals with the minimization of time satisfying given demand. Ingeneral, the quickest multi-commodity flow problems are computationally hard. The outbound lane capacities can be increased through reverting the orientation of lanes towards the demand nodes. We present two approximation algorithms by introducing partial contraow technique in the continuous-time quick estmulti-commodity ow problem: one polynomial-time with the help of length-bounded flow and another FPTAS by using _-condensed time-expanded graph. Both algorithms reverse only necessary arc capacities to get the optimal solutions and save unused arc capacities which may be used for other purposes.   

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