Abstract
We consider a generalization of the maximum flow problem where instead of bounding the amount of flow which passes through an arc, we bound the amount of flow passing “near” an arc. Nearness is specified by an extra distance parameter d. When d=0 we get the usual network flow and d=1 corresponds to bounding the flow through the nodes. A polynomial time algorithm is given to solve the max-flow and min-cost noninterfering flow problems for d=2 and it is shown that the problems become NP-hard for d≥3. A polynomial time algorithm is outlined for arbitrary d when the underlying network is planar and how an integral flow can be obtained from a fractional one. Finally, we describe relationships with induced circuits and perfect graphs, VLSI chip design and the Hilbert basis problem.
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© 1992 Springer-Verlag Berlin Heidelberg
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McDiarmid, C., Reed, B., Schrijver, A., Shepherd, B. (1992). Non-interfering network flows. In: Nurmi, O., Ukkonen, E. (eds) Algorithm Theory — SWAT '92. SWAT 1992. Lecture Notes in Computer Science, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55706-7_21
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DOI: https://doi.org/10.1007/3-540-55706-7_21
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