Universal O(congestion+dilation+\log^{1+\epsilon} N) Local Control Packet Switching Algorithm
Rafail Ostrovsky, Yuval Rabani
Abstract:
In 1988, Leighton, Maggs and Rao proved a much celebrated result: that for any network, given any collection of packets with a specified route for each packet, there exists an "optimal" schedule for all these packets. That is, there exists a schedule of the motion of the packets such that at each step, every edge is crossed by at most one packet, and all the packets are delivered to their destinations in O(C + D) steps, where C is the "congestion" (i.e., the maximum number of paths that share the same edge), and D is the "dilation" (i.e., the length of the longest path). The proof was non-constructive and relied on Lov\'asz Local Lemma. In a followup paper, Leighton and Maggs gave a centralized algorithm for finding the schedule. The original paper left open the question whether there exists a constructive distributed "on-line" algorithm with the same optimal performance.
In this paper, we show a nearly optimal local control algorithm for this long-standing open problem. We show a randomized algorithm which for any network topology delivers all the packets to their destinations in time O(C + D + \log^{1+\epsilon}N) with high probability, where N is the size of the problem, and \epsilon>0 is arbitrary.
comment: Appeared In Proceedings of The Twenty-Ninth ACM Symposium on Theory of Computing (STOC-97)
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