A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman, Bounds on universal sequences, SIAM J. Comput., 18 (1989), pp. 268--277.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....lower bounds is the emphasis of this paper. The current best upper and lower bounds on U (d; n) are summarized in Table 1. See Borodin, Ruzzo, and Tompa [5] for more background. Prior to the current work, the best lower bound for d = 2 was U(2; n) Omega# n log n) due to Bar Noy et al. [4]. This bound is improved in Corollary 3.5 to U(2; n) Omega# n log 4 6 ) Omega# n 1:29 ) For 3 d n=3 0 2, the best previous lower bound was U (d; n) Omega# dn 2 log n d d 2 n 2 ) 3 SIAM Journal on Computing, vol. 21, no. 6, Dec. 1992, 1153 1160. This material is ....

A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman, Bounds on universal sequences, SIAM J. Comput., 18 (1989), pp. 268--277.

....of angles: We have shown the existence of a polynomial length universal sequence of angles (UTSA) for gridded polygons. However we do not know how to find one. The similar question for graphs is also wide open, with the only exceptions (known to us) being paths and cycles [Bridgland 1987] [Bar Noy, Borodin, Karchemer, Linial Werman 1989]. Intuitively, one may think that finding a UTSA in our case is easier, since the robot is assumed to have a kind of compass , while in the UTS problem for graphs, edges are arbitrarily ordered. 5. The minimum memory needed to deterministically cover a region: Counting the total amount of memory ....

A. Bar-Noy, A. Borodin, M. Karchemer, N. Linial, M. Werman, "Bounds on Universal Sequences," SIAM J. Comput. , Vol. 18, No. 2, pp.268-277, (1989).

....traversal sequence of angles: We have shown the existence of a polynomial length universal sequence of angles (UTSA) for gridded polygons. However we do not know how to find one. The similar question for graphs is also wide open, with the only exceptions (known to us) being paths and cycles [9] [8]. Intuitively, one may think that finding a UTSA in our case is easier, since the robot is assumed to have a kind of compass , while in the UTS problem for graphs, edges are arbitrarily ordered. 6 Acknowledgement We would like to thank David Aldous for his advice with respect to the results in ....

A. Bar-Noy, A. Borodin, M. Karchemer, N. Linial, M. Werman, "Bounds on Universal Sequences, " SIAM J. Comput., Vol. 18, No. 2, pp.268-277, (1989).

....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 ....

....the first: for space s, O(n 1=2 log n) s O(n log n) it uses time O( m n) n=s) 2 log 3 n) log( n log n) s) When s = 2(n log n) the time bound is O( m n) log n) only a factor of log n worse than the time optimal bound of depth and breadth first search. As noted in Bar Noy, et al. [4], no previously known deterministic algorithm for ustcon simultaneously achieves polynomial time and sublinear space. Returning to the motivating questions about the relationships among the various space bounded complexity classes, note that if ustcon is solvable deterministically in logarithmic ....

A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman. Bounds on universal sequences. SIAM Journal on Computing, 18(2):268--277, Apr. 1989.

....it is nondeterministic. Several authors have considered 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], 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 ....

A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman. Bounds on universal sequences. SIAM Journal on Computing, 18(2):268--277, Apr. 1989.

....it is nondeterministic. Several authors have considered 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. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman. Bounds on universal sequences. SIAM Journal on Computing, 18(2):268--277, Apr. 1989.

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A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman. Bounds on universal sequences. SIAM Journal on Computing, 18(2):268-- 277, April 1989.

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