H. J. Karloff, R. Paturi, and J. Simon. Universal traversal sequences of length n O(log n) for cliques. Information Processing Letters, 28:241--243, Aug. 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... WAG with an unlimited number of states but only the minimum number (one) of pebbles, a model better known as a universal traversal sequence (Aleliunas et al. 2] Alon et al. 3] Bar Noy et al. 4] Borodin, Ruzzo, and Tompa [16] Bridgland [17] Buss and Tompa [19] Istrail [25] Karloff et al. [26], Tompa [33] A result of Borodin, Ruzzo, and Tompa [16] shows that such an automaton requires ) time (on regular graphs with 3n=2 m n =60n) Thus, for the particularly weak version of logarithmic space corresponding to the case P = 1, a quadratic lower bound on time is known. The known ....

H. J. Karloff, R. Paturi, and J. Simon. Universal traversal sequences of length n O(log n) for cliques. Information Processing Letters, 28:241--243, Aug. 1988.

....traversal sequences of polynomial length exist for undirected graphs. Upper and lower bounds on the length of UTS s are known for various types of graphs [AAR90, BNBK 89, BRT89, HW89, Tom90] Some authors show how to construct superpolynomial length sequences [BNS89, BNBK 89, Bri87, KPS88, Nis90] and Istrail shows how to construct polynomial length sequences for certain classes of graphs [Ist88, Ist90] If one could construct polynomial length UTS s for arbitrary graphs in space O(log n) this would give an O(log n) space algorithm for ustcon, since a UTS can easily be followed ....

H. J. Karloff, R. Paturi, and J. Simon. Universal traversal sequences of length n O(logn) for cliques. Information Processing Letters, 28:241--243, August 1988.

.... JAG with an unlimited number of states but only the minimum number (one) of pebbles, a model better known as a universal traversal sequence (Aleliunas et al. 2] Alon et al. 3] Bar Noy et al. 4] Borodin, Ruzzo, and Tompa [18] Bridgland [19] Buss and Tompa [21] Istrail [34] Karloff et al. [37], Tompa [49] A result of Borodin, Ruzzo, and Tompa [18] shows that such an automaton requires Omega Gamma m 2 ) time (on regular graphs with 3n=2 m n 2 =6 Gamma n) Thus, for the particularly weak version of logarithmic space corresponding to the case P = 1, a quadratic lower bound on ....

H. J. Karloff, R. Paturi, and J. Simon. Universal traversal sequences of length n O(log n) for cliques. Information Processing Letters, 28:241--243, Aug. 1988.

....is possible is still an open problem. There are two interesting partial results that are worth mentioning. For d = 2, Istrail [4] gives a construction of polynomial length traversal sequences, but his sequences cannot be constructed in deterministic logspace. For d = n Gamma 1, Karloff et al. [5] give an explicit construction of traversal sequences of length n O(logn) Traversal Sequences and Pseudorandom Generators. The best explicit universal traversal sequences constructed so far are due to Nisan [7] This construction exploits a connection, due to Babai et al. 2] between ....

H. Karloff, R. Paturi, J. Simon, Universal Traversal Sequences of Length n O(logn) for Cliques, Information Processing Letters, 28 (1988), pp. 241--243

....is solvable by a deterministic logarithmic space algorithm, and perhaps showing this would be an easier first step towards the main goal. In fact, considerable effort has been expended on this step, for example in studying and attempting to constructively generate universal traversal sequences [1, 2, 3, 4, 8, 9, 12, 13, 14, 15, 19, 25]. Alternatively, if deterministic and nondeterministic classes are distinct, then ustcon is a likely candidate for a problem that will separate the classes. In either case, its complexity is of interest. Settling the deterministic space complexity of ustcon is a very difficult open problem. A ....

H. J. Karloff, R. Paturi, and J. Simon. Universal traversal sequences of length n O(logn) for cliques. Information Processing Letters, 28:241--243, Aug. 1988.

.... traversal of undirected regular graphs by a JAG with an unlimited number of states but only the minimum number (one) of pebbles, a model better known as a universal traversal sequence (Aleliunas et al. 2] Alon et al. 3] Bar Noy et al. 4] Bridgland [15] Istrail [25] Karloff et al. [28]) A result of Borodin, Ruzzo, and Tompa [14] shows that such an automaton requires Omega0 m 2 ) time (on regular graphs with 3n=2 m n 2 =6 0 n) Thus, for the particularly weak version of logarithmic space corresponding to the case P = 1, a quadratic lower bound on time is known. The known ....

H. J. Karloff, R. Paturi, and J. Simon. Universal traversal sequences of length n O(logn) for cliques. Information Processing Letters, 28:241--243, Aug. 1988.

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