J. Buss, and M. Tompa, Lower bounds on universal traversal sequences based on chains of length ve, Information and Computation, 120(2):326-329, 1995. Home/Search Document Details and Download
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Tree Exploration with Little Memory - Krzysztof Diks Pierre (2002) (Correct)
....labels, such that the path guided by this sequence visits all edges of any graph. It is known that, with high probability, a sequence of length d log n) chosen uniformly at random, guides a walk in any d regular (connected) graph of n nodes. Explicit UTS are known for 2 regular graphs (cf. [6, 12, 13, 19, 21]) for 3 regular graphs (cf. 4, 18, 23] for cliques (cf. 2, 20] and for expanders (cf. 17] Some of these sequences can be constructed in log space, and hence can produce perpetual exploration with compact memory. However, without the a priori knowledge of n, non of these constructions ....
J. Buss, and M. Tompa, Lower bounds on universal traversal sequences based on chains of length ve, Information and Computation, 120(2):326-329, 1995. 19
A Time-Space Tradeoff for Undirected Graph.. - Beame, Borodin.. (1997) (5 citations) Self-citation (Tompa) (Correct)
.... of undirected regular graphs by a 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 ....
J. Buss and M. Tompa. Lower bounds on universal traversal sequences based on chains of length five. Information and Computation, 120(2):326--329, Aug. 1995.
Time-Space Tradeoffs for Undirected Graph.. - Beame, Borodin.. (1997) (5 citations) Self-citation (Tompa) (Correct)
.... 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] 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 ....
....more vertices. 2 Using similar techniques, Theorem 19 proves that the previous result in fact holds for any even length ff such that ff is not a universal traversal sequence for all labeled (n=2) cycles. For instance, it holds for any ff whose length is even and O(n 1:43 ) Buss and Tompa [21]) Theorem 19: For any ff 2 f0; 1g of even length, any even integer n, and any integer k, if ff is not a universal traversal sequence for all labeled (n=2) cycles, then ff k is not a universal traversal sequence for all labeled n cycles. Proof: Since ff is not a universal traversal sequence ....
J. Buss and M. Tompa. Lower bounds on universal traversal sequences based on chains of length five. Information and Computation, 120(2):326--329, Aug. 1995.
Tree Exploration with Little Memory - Krzysztof Diks Pierre (2002) (Correct)
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J. Buss, and M. Tompa, Lower bounds on universal traversal sequences based on chains of length ve, Information and Computation, 120(2):326-329, 1995.
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