Abstract
Consider a simple network flow problem in which a flow of value D must be split among n channels directed from a source to a sink. The initially unknown channel capacities can be probed by attempting to send a flow of at most D units through the network. If the flow is not feasible, we are told on which channels the capacity was exceeded (binary feedback) and possibly also how many units of flow were successfully sent on these channels (throughput feedback). For throughput feedback we present optimal protocols for minimizing the number of rounds needed to find a feasible flow and for minimizing the total amount of wasted flow. For binary feedback we present an asymptotically optimal protocol.
An extended abstract of this paper was presented at the graco 2005 conference [6].
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References
Chandrayana, K., Zhang, Y., Roughan, M., Sen, S., Karp, R.: Search game in inter-domain traffic engineering (2004) (manuscript)
Chiu, D., Jain, R.: Analysis of the increase/decrease algorithms for congestion avoidance in computer networks. J. of Comput. Networks and ISDN 17(1), 1–14 (1989)
Garg, N., Young, N.E.: On-line end-to-end congestion control. In: Proc. of FOCS 2002, pp. 303–312 (2002)
Jacobson, V.: Congestion avoidance and control. In: Proc. of ACM SIGCOMM 1988, pp. 314–329 (1988)
Karp, R., Koutsoupias, E., Papadimitriou, C., Shenker, S.: Combinatorial optimization in congestion control. In: Proc. of FOCS 2000, pp. 66–74 (2000)
Karp, R., Nierhoff, T., Tantau, T.: Optimal Flow Distribution Among Multiple Channels with Unknown Capacities. In: Proc. of GRACO 2005. Electronic Notes in Discrete Mathematics, vol. 19, pp. 225–231. Elsevier, Amsterdam (2005)
Low, S.H., Paganini, F., Doyle, J.C.: Internet congestion control: An analytical perspective. IEEE Control Systems Magazine, 28–43 (February 2002)
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Karp, R., Nierhoff, T., Tantau, T. (2006). Optimal Flow Distribution Among Multiple Channels with Unknown Capacities. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 3895. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11685654_4
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DOI: https://doi.org/10.1007/11685654_4
Publisher Name: Springer, Berlin, Heidelberg
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