M. Luby. Removing randomness in parallel without processor penalty. Journal of Computer and System Sciences, 47(2):250-286, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....one might aim at the more modest goal of computing reasonably good colourings, instead of optimal ones. By a trivial modi cation of a well known vertex colouring algorithm of Luby it is possible to edge colour a graph using 2 2 colours in O(log n) rounds (where n is the number of processors) [4]. We shall present and analyze a simple localised distributed algorithm that compute near optimal edge colourings. The algorithm proceeds in a sequence of rounds. In each round, a simple randomised heuristic is invoked to colour a signi cant fraction of the edges successfully. The remaining edges ....

Luby, M.: Removing randomness in parallel without a processor penalty. J. Computer and Systems Sciences 47:2 (1993) 250-286.

....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 ....

M. Luby, Removing randomness in parallel without processor penalty, Journal of Computer and System Sciences, 47(2):250-286, October 1993

....one might aim at the more modest goal of computing reasonably good 3 colourings, instead of optimal ones. By a trivial modi cation of a well known vertex colouring algorithm of Luby it is possible to edge colour a graph using 2 2 colours in O(log n) rounds (where n is the number of processors) [6]. We shall present and analyze two classes of simple localised distributed algorithms that compute near optimal edge colourings. Both algorithms proceed in a sequence of rounds. In each round, a simple randomised heuristic is invoked to colour a signi cant fraction of the edges successfully. The ....

Luby, M.: Removing randomness in parallel without a processor penalty. J. Computer and Systems Sciences 47:2 (1993) 250-286.

....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 every uncoloured vertex is asleep. Each such vertex awakes with probability p and executes a trivial attempt (in Luby s paper p = 1=2) Then, whether or not the vertex awoke, the palette undergoes a trivial update. ....

M. Luby, Removing randomness in parallel without processor penalty, Journal of Computer and System Sciences, 47(2) (1993), 250--286.

....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 every uncoloured vertex is asleep. Each such vertex awakes with probability p and executes a trivial attempt (in Luby s paper p = 1 2 ) Then, whether or not the vertex awoke, the palette undergoes a trivial ....

M. Luby, Removing randomness in parallel without processor penalty, Journal of Computer and System Sciences, 47(2) (1993), 250--286.

....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 ....

M. Luby, Removing randomness in parallel without processor penalty, Journal of Computer and System Sciences, 47(2):250-286, October 1993

....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 ....

M. Luby, Removing randomness in parallel without processor penalty, Journal of Computer and System Sciences, 47(2):250-286, October 1993

....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 every uncoloured vertex is asleep. Each such vertex awakes with probability p and executes a trivial attempt (in Luby s paper p = 1=2) Then, whether or not the vertex awoke, the palette undergoes a trivial update. ....

M. Luby, Removing randomness in parallel without processor penalty, Journal of Computer and System Sciences, 47(2) (1993), 250--286.

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M. Luby. Removing randomness in parallel without processor penalty. Journal of Computer and System Sciences, 47(2):250-286, 1993.

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