| A. Borodin, W.L. Ruzzo, and M. Tompa. Lower bounds on the length of universal sequences. In Proceedings of the 21st ACM Symposium on the Theory of Computing, pages 562--573. |
....traversal sequence (UTS) for G(d,n) if U traverses every G G(d,n) starting at any vertex in G. Let U(d,n) denote the length of a shortest UTS for non empty G(d,n) and define U(d,n) U(d,n 1) in case G(d,n) is empty. The lower and upper bounds on U(d,n) for various ranges of d were studied in [1, 2, 3, 5, 8, 10, 12]. Prior to the current work, the best lower bounds on U(d,n) for d=2 and for 3 d n 17 1 were U(2,n) W(n log 5 10 ) and U(d,n) W(d 2 log 5 10 n 1 log 5 10 ) due to a personal communication [6] These lower bounds are improved in this paper to U(2,n) W(n log 7 17.82 ) and U(d,n) ....
A. Borodin, W.L. Ruzzo, and M. Tompa. Lower bounds on the length of universal sequences. In Proceedings of the 21st ACM Symposium on the Theory of Computing, pages 562--573.
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