Abstract
We study packet routing problems, in which we are given a set of N packets which will be sent on preselected paths with congestion C and dilation D. For store-and-forward routing, in which nodes have buffers for packets in transit, there are routing algorithms with a performance that matches the lower bound Ω(C+D). Motivated from optical networks, we study hot-potato routing in which the nodes are bufferless. Due to the lack of buffers, in hot-potato routing the packets may be delayed more than in store-and-forward routing. An interesting question is how much is the performance of routing algorithms affected by the absence of buffers. Here, we answer this question for the class of leveled networks, in which the nodes are partitioned into L+1 distinct levels. We present a randomized hot-potato routing algorithm for leveled networks, which routes the packets in O((C + L) ln9 (LN)) time with high probability. For routing problems with dilation Ω(L), and where N is a polynonial in L, this bound is within polylogarithmic factors of the lower bound Ω(C+L). Our algorithm demonstrates that for such routing problems the benefit from using buffers is no more than polylogarithmic; thus, hot-potato routing is an efficient way to route packets in leveled networks. In hot-potato routing, due to the lack of buffers, the packets may not be able to remain on their preselected paths during the course of routing (while in store-and-forward routing the packets remain on their preselected paths). However, in our algorithm the actual path that each packet follows contains its original preselected path; thus the lower bound Ω(C+L) is also a lower bound for the new paths. Our algorithm is distributed, that is, routing decisions are taken locally at each node while packets are routed in the network. To our knowledge, this is the first hot-potato algorithm designed and analyzed, in terms of congestion and dilation, for leveled networks.
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Busch, C. Õ(Congestion + Dilation) Hot-Potato Routing on Leveled Networks. Theory Comput Syst 37, 371–396 (2004). https://doi.org/10.1007/s00224-004-1136-8
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DOI: https://doi.org/10.1007/s00224-004-1136-8