Combinatorial Algorithms for the Generalized Circulation Problem

A generalization of the maximum-flow problem is considered in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e) lambda (e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. Conservation of flow is required at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. The authors present polynomial-time combinatorial algorithms for this problem. The algorithms are simple and intuitive. >

Authors

• Andrew V. Goldberg
• Serge A. Plotkin
• Éva Tardos

Keywords

• Polynomials
• Computer science
• Contracts
• Costs
• Exchange rates
• Linear programming
• Security
• Laboratories
• Mathematics
• Algorithm design and analysis
• Combination Of Algorithms
• Non-negative
• Running Time
• Exchange Rate
• Shortest Path
• End Of Phase
• Reachable
• Finite Time
• Directed Graph
• Nodes In The Graph
• Residual Network
• Maximum Flow
• Flow Values
• Flow Problem
• Problem Instances
• Source Node
• Amount Of Flow
• Polynomial-time Algorithm