O. Johansson, personal communication.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....can be computed in O(polylog(n) rounds. Furthermore, these randomized algorithms are usually extremely simple and their actual complexity is very low. For instance, Delta 1) vertex coloring and MIS can be computed in O(log n) rounds with high probability by exceedingly simple protocols [16, 17, 21]. Another important case is that of (O(log n) O(log n) decompositions, a very interesting type of graph decomposition with many applications, which can be computed in O(log n) rounds [15] In fact, there exist non trivial functions, such as nearly optimal edge colourings, that can be ....

O. Johansson, personal communication.

....we shall refer to this as the trivial algorithm. The trivial algorithm always computes a valid colouring regardless of the composition of the initial lists, and does so in O(log n) rounds with high probability that is, with probability approaching 1 as the number of vertices increases [10, 13, 4]. It is apparent that the trivial algorithm is distributed, since each vertex only relies on information from the neighbouring vertices. The well known distributed algorithm for the same problem given by Luby [15] amends the trivial algorithm in the following way: at the beginning of each round ....

....the algorithm sufficiently to show that with high probability there exist a round i = O(k) such that, for every vertex u, a i (u) deg i (u) 1: 1) This will occur after the algorithm has switched to its trivial phase. Since the behaviour of the trivial algorithm in this situation is known [10, 13, 4], 5 we can then immediately conclude that the trivial algorithm will with certainty complete the colouring and it will do so within O(log n) rounds with high probability. As stated in the introduction, with a little bit more work it is possible to show that the running time is actually O(k log ....

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O. Johansson, Personal communication, May 1997. 19

....we shall refer to this as the trivial algorithm. The trivial algorithm always computes a valid colouring regardless of the composition of the initial lists, and does so in O(log n) rounds with high probability that is, with probability approaching 1 as the number of vertices increases [13]. It is apparent that the trivial algorithm is distributed, since each vertex only relies on information from the neighbouring vertices. The well known distributed algorithm for the same problem given by Luby [18] amends the trivial algorithm in the following way: at the beginning of each round ....

....refer to this as the termination condition. This will occur after the algorithm has switched to its trivial phase. It is known that if the graph satisfies condition 5 the trivial algorithm will with certainty complete the colouring and it will do so within O(log n) rounds with high probability [13]. Therefore, if we prove that the termination condition is attained in O(k) rounds with high probability, we can conclude that the dozing off algorithm succeeds in O(k log n) rounds with high probability a slightly weaker version of Theorem 1. As stated in the introduction, with a little bit ....

[Article contains additional citation context not shown here]

O. Johansson, Personal communication, May 1997.

....computed in polylogarithmically many rounds. Furthermore, these randomized algorithms are usually extremely simple and their actual complexity is very low. For instance, Delta 1) vertex coloring and MIS can be computed in O(log n) rounds with high probability by exceedingly simple protocols [18, 19, 23]. Another important case is that of (O(log n) O(log n) decompositions, a very interesting type of graph decomposition with many applications, which can be computed in O(log 2 n) rounds [17] In fact, there exist non trivial functions, such as nearly optimal edge colourings, that can be ....

O. Johansson, personal communication.

....can be computed in O(polylog(n) rounds. Furthermore, these randomized algorithms are usually extremely simple and their actual complexity is very low. For instance, Delta 1) vertex coloring and MIS can be computed in O(log n) rounds with high probability by exceedingly simple protocols [17, 18, 22]. Another important case is that of (O(log n) O(log n) decompositions, a very interesting type of graph decomposition with many applications, which can be computed in O(log 2 n) rounds [16] In fact, there exist non trivial functions, such as nearly optimal edge colourings, that can be ....

O. Johansson, personal communication.

....we shall refer to this as the trivial algorithm. The trivial algorithm always computes a valid colouring regardless of the composition of the initial lists, and does so in O(log n) rounds with high probability that is, with probability approaching 1 as the number of vertices increases [10, 13, 4]. It is apparent that the trivial algorithm is distributed, since each vertex only relies on information from the neighbouring vertices. The well known distributed algorithm for the same problem given by Luby [15] amends the trivial algorithm in the following way: at the beginning of each round ....

....the algorithm sufficiently to show that with high probability there exist a round i = O(k) such that, for every vertex u, a i (u) deg i (u) 1: 1) This will occur after the algorithm has switched to its trivial phase. Since the behaviour of the trivial algorithm in this situation is known [10, 13, 4], we can then immediately conclude that the trivial algorithm will with certainty complete the colouring and it will do so within O(log n) rounds with high probability. As stated in the introduction, with a little bit more work it is possible to show that the running time is actually O(k log n= ....

[Article contains additional citation context not shown here]

O. Johansson, Personal communication, May 1997.

....and target tagset; this symbolic patching of the statistical model approach minimises the linguistic expertise we need to capture (and first develop ) to devise symbolic mapping rules. We have learnt of corpus tagset mapping work by a number of other researchers (including [13] 30] 20] [39] [41] 52] but generally such research in the past has been merely a means to an end (to create a re tagged Corpus) so the full mapping algorithms have not been formalised or published; but if all we need is a limited nuber of mapping rules to patch the Markov model then we may be able to ....

Stig Johansson. 1994. personal communication.

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