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ACM Transactions on Algorithms (TALG)
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The paper constructs the first polynomial universal traversing sequences for cycles, solving an open problem of S. Cook and R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, C. Rackoff (1979) [2] in the case of 2-regular graphs. The existence of universal traversing sequences of size &Ogr;(d2n3logn) for n-vertex d-regular graphs was established in [2] by a probabilistic argument, which was inherently non-constructive. For the cycles, the non-constructive upper bound was improved to &Ogr; (n3) by Janowsky (1983) [13] and Cobham (1986) [8]. Previously, the best explicit constructions for cycles were due to Bridgland (1986) and A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman (1986), and have size &Ogr;(nlog n).Our universal traversing sequence has size &Ogr;(n4.76), and can be constructed in log-space.