Integer Flow with Multipliers: The Special Case of Multipliers 1 and 2
نویسندگان
چکیده
The problem to find a valid integer flow with flow multipliers on nodes or arcs is long known to be NP-complete [10]. We show that the problem is still hard when restricted to instances with a limited number of integral multipliers. To find an integer minimum cost maximal pseudoflow, respecting only the node balance constraints of the inner nodes, is also still a difficult task. Further, we demonstrate that for the multipliers 1 and 2 optimal solutions with fractions 1 2n , n ∈ N can occur. For special instances which are motivated by some applications we prove that the optimal solution is halfintegral. Finally, we extend the Successive Shortest Path Algorithm [2, 7, 9], to the minimum cost flow problem with multipliers. For the application based instances with halfintegral optimal solutions, we try to find acceptable integral solutions.
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