Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Fiber Network Service Survivability
Fiber Network Service Survivability
Routing restorable bandwidth guaranteed connections using maximum 2-route flows
IEEE/ACM Transactions on Networking (TON)
Multiroute flow problem
Algorithms for 2-Route Cut Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Experimental evaluation of solution approaches for the K-route maximum flow problem
Computers and Operations Research
| Hi-index | 0.00 |
In a directed flow network we assign capacities on vertices as well as on edges. We consider a (δ, η)-balanced flow problem of single commodity case. A (δ, η)-balanced flow is defined as a flow such that the flow value at each edge is not more than δ, ċ f and the flow value at each vertex is not more than η ċ f, where f is the total amount of the flow. Based on (δ, η)-balanced flow, the (δ, η)- capacity is defined for a mixed cut in a network. A mixed cut in a network is a set of edges and vertices removal of those separates the network. Then the max-flow min-cut theorem for this (δ, η)-balanced flow is proved for the single commodity case in a directed network. The theorem for (δ, η)-balanced flow is not easily to be proved by only applying the max-flow min-cut theorem of ordinary flows. Then we show a method for evaluating the maximum (δ, η)-balanced flow. The algorithm gives the maximum value of (δ, η)-balanced flow between s and t in N with at most |V| ċ |E| evaluations of maximum flow in a network, where V is the vertex set of N and E is the edge set of N, respectively. Each evaluations of the maximum flow is performed in N with altered capacities on edges and on vertices. We can apply all the results to undirected networks.