Abstract
In this paper we study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. The flow of each commodity can be split on several paths. Arcs are equipped with load dependent price functions defining routing costs. We discuss a greedy online algorithm that routes each commodity by minimizing a convex cost function that only depends on the demands previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is \(\tfrac{4K}{2+K}\)-competitive, where K is the number of commodities. For the parallel arc case, this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.
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Harks, T., Heinz, S., Pfetsch, M.E. (2007). Competitive Online Multicommodity Routing. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_19
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DOI: https://doi.org/10.1007/11970125_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69513-4
Online ISBN: 978-3-540-69514-1
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