A Fast Algorithm For Finding A Maximum Free Multiflow In An Inner Eulerian Network And Some Generalizations

be a network, where is an undirected graph with nodes and edges, is a set of specified nodes of , called terminals, and each edge of has a nonnegative integer capacity . If the total capacity of edges with one end at is even for every non-terminal node , then is called inner Eulerian. A free multiflow is a collection of flows between arbitrary pairs of terminals such that the total flow through each edge does not exceed its capacity.

In this paper we first generalize a method in Karzanov [11] to find a maximum integer free multiflow in an inner Eulerian network, in time, where is the complexity of finding a maximum flow between two terminals. Next we extend our algorithm to solve the so-called laminar locking problem on multiflows, also in time.

We then consider analogs of the above problems in inner balanced directed networks, which means that for each non-terminal node , the sums of capacities of arcs entering and leaving are the same. We show that for such a network a maximum integer free multiflow can be constructed in time, and then extend this result to the corresponding locking problem.

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Received: March 24, 1997

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Ibaraki, T., Karzanov, A. & Nagamochi, H. A Fast Algorithm For Finding A Maximum Free Multiflow In An Inner Eulerian Network And Some Generalizations. Combinatorica 18, 61–83 (1998). https://doi.org/10.1007/PL00009811

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  • AMS Subject Classification (1991) Classes:  90C27; 90B10