document: Two efficient algorithms for the generalized maximum balanced flow problem Minoux -LRB- 1976 -RRB- considered the maximum balanced flow problem , i.e. the problem of finding a maximum flow in a two-terminal network N = -LRB- V , A -RRB- with source s and sink t satisfying the constraint that any arc-flow of N is bounded by a fixed proportion of the total flow value from s to t , where V is vertex set and A is arc set . As a generalization , we focus on the problem of maximizing the total flow value of a generalized flow in N with gains gamma -LRB- a -RRB- > 0 -LRB- a in A -RRB- where any arc-flow is bounded by a fixed proportion of the total flow value , where gamma -LRB- a -RRB- f -LRB- a -RRB- units arrive at the vertex w for each arc-flow f -LRB- a -RRB- -LRB- a identical to -LRB- upsilon , w -RRB- in A -RRB- entering vertex upsilon in a generalized flow . Our main results are to propose two polynomial algorithms for this problem . The first algorithm runs in O -LRB- mM -LRB- n , m , B ' -RRB- log B -RRB- time , where B is the maximum absolute value among integral values used by an instance of the problem , and M -LRB- n , m , B ' -RRB- denotes the complexity of solving a generalized maximum flow problem in a network with n vertices , and m arcs , and a rational instance expressed with integers between 1 and B ' . In the second algorithm , using a parameterized technique , runs in O -LRB- -LCB- M -LRB- n , m , B ' -RRB- -RCB- / sup 2 / -RRB- time
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extractive_keyphrases: generalized maximum balanced flow problem polynomial algorithms parameterized technique
abstractive_keyphrases: two-terminal network