N. Alon, Y. Azar, and Y. Ravid, Universal sequences for complete graphs, Discrete Applied Mathematics, 27:25-28, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 allows the robot to return to its original position, or even to stop. ....

N. Alon, Y. Azar, and Y. Ravid, Universal sequences for complete graphs, Discrete Applied Mathematics, 27:25-28, 1990.

....as a WAG walking automaton for graphs . Several authors have considered traversal 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 ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

....as traversal sequences, and moreover, they also exhibit a new property the ability to backtrack. Using that new ability we construct universal exploration sequences (UXS) for some classes of graphs. These UXS s beat lower bounds on the length of UTS s for cycles and cliques given by [BBK ] [AAR], T] and [BT] Under our definition it can be shown, that a random exploration sequence of length O(d 2 n 3 log n) is a UXS for d regular graphs with high probability. Thus, constructions of UTS s of length n O(log n) for 3 regular graphs that are based on pseudo random generators apply to ....

N. Alon, Y. Azar, and Y. Ravid, Universal sequences for complete graphs, Discrete Appl. Math, 27, pp. 25-28, 1990.

.... = O(n 3 log n) n=2 0 1 d Chandra et al. 6] U (d; n) Omega# n 1:29 ) d = 2 This paper U (d; n) Omega# d 0:71 n 2:29 ) 3 d n log 6 1:5 This paper U (d; n) Omega# d 2 n 2 ) n log 6 1:5 d n=3 0 2 Borodin et al. 5] U (d; n) Omega# n 2 ) n=3 0 2 d Alon et al. [3] due to Borodin, Ruzzo, and Tompa [5] This bound is improved in Corollary 3.6 to U (d; n) Omega# d 20log 4 6 n 1 log 4 6 d 2 n 2 ) Omega# d 0:71 n 2:29 d 2 n 2 ) The value of d at which the second term begins to dominate is d = n log 6 1:5 n 0:23 . By a clever ....

N. Alon, Y. Azar, and Y. Ravid, Universal sequences for complete graphs, Discrete Applied Mathematics, 27 (1990), pp. 25--28.

.... n) O(n 3 log n) n=2 0 1 d Chandra et al. 5] U(d; n) Omega# n 1:43 ) d = 2 This paper U(d; n) Omega# d 0:57 n 2:43 ) 3 d n log 10 2 This paper U(d; n) Omega# d 2 n 2 ) n log 10 2 d n=3 0 2 Borodin et al. 4] U(d; n) Omega# n 2 ) n=3 0 2 d Alon et al. [3] For 3 d n=3 0 2, the best previous lower bound was U(d; n) Omega# d 0:67 n 2:33 d 2 n 2 ) the first term due to Coppersmith (see Tompa [7] and the second term due to Borodin, Ruzzo, and Tompa [4] This bound is improved in Corollary 9 to U(d; n) Omega# d 20log 5 10 n ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

....to show that UTS s for directed graphs are of exponential length, Aleliunas et al. AKL 79] prove (nonconstructively) that universal 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 ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

.... d Chandra et al. 5] U(d; n) Omega Gamma n 1:43 ) d = 2 This paper U(d; n) Omega Gamma d 0:57 n 2:43 ) 3 d n log 10 2 This paper U(d; n) Omega Gamma d 2 n 2 ) n log 10 2 d n=3 Gamma 2 Borodin et al. 4] U(d; n) Omega Gamma n 2 ) n=3 Gamma 2 d Alon et al. [3] For 3 d n=3 Gamma 2, the best previous lower bound was U(d; n) Omega Gamma d 0:67 n 2:33 d 2 n 2 ) the first term due to Coppersmith (see Tompa [7] and the second term due to Borodin, Ruzzo, and Tompa [4] This bound is improved in Corollary 8 to U(d; n) Omega Gamma d ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

....dimension, namely, 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) ....

.... of edge labeled graphs, and define C V (F) to be the maximum cover time of any graph in F , and similarly for H V (F ) A basic result of Aleliunas et al. 2] is that any family F of d regular graphs has a (vertex) universal traversal sequence of length O(C V (F) log(n 2 jF j) Alon et al. [3] and Chandra et al. 22] observe that C V (F) can be replaced by H V (F) in this expression. These results extend easily to universal traversal sequences for nonregular graphs of maximum degree d (as defined above) by observing that cover and hitting times are at most doubled when the random walk ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

....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 ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

....dimension, namely, 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 ....

.... of edge labeled graphs, and define C V (F) to be the maximum cover time of any graph in F , and similarly for H V (F) A basic result of Aleliunas et al. 2] is that any family F of d regular graphs has a (vertex) universal traversal sequence of length O(C V (F) log(n 2 jF j) Alon et al. [3] and Chandra et al. 17] observe that C V (F) can be replaced by H V (F) in this expression. These results extend easily to universal traversal sequences for nonregular graphs of maximum degree d (as defined above) by observing that cover and hitting times are at most doubled when the random walk ....

N. Alon, Y. Azar, and Y. Ravid. Universal sequences for complete graphs. Discrete Applied Mathematics, 27:25--28, 1990.

No context found.

N. Alon, Y. Azar, and Y. Ravid, Universal sequences for complete graphs, Discrete Applied Mathematics, 27:25-28, 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC