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We study multipacket routing problems. We divide the multipacket routing problem into two classes, namely, distance limited and bisection limited routing problems. Then, we concentrate on rings of processors. We prove a new lower bound of 2n/ 3 routing steps for the case of distance limited routing problems. We also give an algorithm that tightens this lower bound. For bisection limited problems the lower bound is kn/ 4,k >2, where k is the number of packets per processor. The trivial algorithm needs in the worst case k | n /2| steps to terminate. An algorithm that completes the routing in kn /4 + 2.5 n routing steps is given. We define the class of pure routing algorithms and we demonstrate that new lower bounds hold if the routing is to be done by an algorithm in this class.
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Fillia Makedon and Antonios Symvonis, "Optimal Algorithms for Multipacket Routing Problems on Rings." Dartmouth Computer Science Technical Report PCS-TR91-174, 1991.
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