A. Panconesi and A. Srinivasan. On the complexity of distributed network decomposition. Journal of Algorithms, 20:356-374, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....In fact, many of these algorithms are very satisfactory because they are both quite simple and really of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing from bounded degree graphs to general topologies has proven elusive, in spite of several efforts [1, 2, 15, 20, 23, 24]. The situation here is, more or less, as follows. For a reasonably large class of graph structures, the asymptotically best deterministic algorithm known to date uses O(n ffl(n) rounds, where ffl(n) is a function which (very slowly) goes to 0 as n, the size of the network, grows. These ....

A. Panconesi and A. Srinivasan, On the complexity of Distributed Network Decomposition, Journal of Algorithms 20, 356--374 (

....was previously shown in [6] only for graphs of constant degree. Linial [9] asked whether this quadratic bound can be improved at the cost of increasing time from O(log n) to, e.g. polylogarithmic. Both randomized and deterministic distributed vertex and edge coloring have been also studied in [1, 7, 12, 13]. For edge coloring, the best randomized algorithm is a O(log log n) time algorithm achieving a (1 ffl) Delta coloring [7] where ffl is any given positive constant. For the deterministic case, the best known edge coloring algorithm has time complexity 2 O( p log n) 12] On the other hand, ....

....hand, for vertex coloring, there are randomized and deterministic algorithms that use Delta 1 or Delta colors. For the randomized case, the fastest algorithm known so far is polylogarithmic [10, 12] and for the deterministic case, the fastest one has time complexity O(n O(1= p log n) [13]. Our results. Our main result is a deterministic O( Delta) vertex coloring algorithm working in O(log (n= Delta) rounds. Thus we improve both the number of colors and execution time of [9] Consequently we give a strong positive answer to Linial s question. To the best of our knowledge, ours ....

A. Panconesi and A. Srinivasan, On the complexity of distributed network decomposition, in Journal of Algorithms, 20, 1996, pp. 356-374.

....In fact, many of these algorithms are very satisfactory because they are both quite simple and really of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing from bounded degree graphs to general topologies has proven elusive, in spite of several efforts [1, 2, 17, 22, 25, 26]. The situation here is, more or less, as follows. For a reasonably large class of graph structures, the asymptotically best deterministic algorithm known to date uses O(n ffl(n) rounds, where ffl(n) is a function which (very slowly) goes to 0 as n, the size of the network, grows. These ....

A. Panconesi and A. Srinivasan, On the complexity of Distributed Network Decomposition, Journal of Algorithms 20, 356--374 (1996).

.... from the uncoloured vertex [17] It is an open problem whether randomization is necessary in all of the above algorithmic results; the asymptotically best deterministic protocols known to date need O(n ffl(n) rounds, where ffl(n) tends (very slowly) to zero as the number of vertices grows [1, 18]. In a 1968 paper Vizing asked whether upper bounds for the chromatic number better than those given by Brooks Theorem existed, provided some sparsity conditions were satisfied. In particular, he asked what happens for triangle free graphs. We shall refer to colourings of trianglefree graphs ....

A. Panconesi and A. Srinivasan, On the complexity of distributed network decomposition, Journal of Algorithms 20 (

.... from the uncoloured vertex [21] It is an open problem whether randomization is necessary in all of the above algorithmic results; the asymptotically best deterministic protocols known to date need O(n ffl(n) rounds, where ffl(n) tends (very slowly) to zero as the number of vertices grows [1, 22]. In a 1968 paper Vizing asked whether upper bounds for the chromatic number better than those given by Brooks Theorem existed, provided some sparsity conditions were satisfied. In particular, he asked what happens for triangle free graphs. We shall refer to colourings of triangle free graphs ....

A. Panconesi and A. Srinivasan, On the complexity of distributed network decomposition, Journal of Algorithms 20 (1996), 356--374.

....In fact, many of these algorithms are very satisfactory because they are both quite simple and really of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing from bounded degree graphs to general topologies has proven elusive, in spite of several efforts [1, 2, 16, 21, 23, 24]. The situation here is, more or less, as follows. For a reasonably large class of graph structures, the asymptotically best deterministic algorithm known to date uses O(n ffl(n) rounds, where ffl(n) is a function which (very slowly) goes to 0 as n, the size of the network, grows. These ....

A. Panconesi and A. Srinivasan, On the complexity of Distributed Network Decomposition, Journal of Algorithms 20, 356--374 (1996).

.... from the uncoloured vertex [17] It is an open problem whether randomization is necessary in all of the above algorithmic results; the asymptotically best deterministic protocols known to date need O(n ffl(n) rounds, where ffl(n) tends (very slowly) to zero as the number of vertices grows [1, 18]. In a 1968 paper Vizing asked whether upper bounds for the chromatic number better than those given by Brooks Theorem existed, provided some sparsity conditions were satisfied. In particular, he asked what happens for triangle free graphs. We shall refer to colourings of triangle free graphs ....

A. Panconesi and A. Srinivasan, On the complexity of distributed network decomposition, Journal of Algorithms 20 (1996), 356--374.

.... graph functions, including maximal independent sets and matchings, vertex colourings and network decomposition, the best determinstic algorithms known so far have time complexity O(n ffl(n) where n is the number of vertices of the network and ffl(n) is a function which goes to zero as n grows [4, 23]. On the other hand, if randomization is allowed all of these functions can be computed in O(polylog n) time [18, 15, 20, 25] This paper shows that the improvement brought by randomization can be as big as doubly exponential. The question remains whether this is inherently the case. We believe ....

A. Panconesi and A. Srinivasan, On the complexity of distributed network decomposition, Journal of Algorithms 20 (1996), 356--374.

.... functions, including maximal independent sets and matchings, vertex colourings and network decomposition, the best determinstic algorithms known so far have time complexity O(n ffl(n) where n is the number of vertices of the network and ffl(n) is a function which goes to zero 3 as n grows [4, 24]. On the other hand, if randomization is allowed all of these functions can be computed in O(polylog n) time [19, 16, 21, 26] This paper shows that the improvement brought by randomization can be as big as doubly exponential. The question remains whether this is inherently the case. We believe ....

A. Panconesi and A. Srinivasan, On the complexity of distributed network decomposition, Journal of Algorithms 20 (1996), 356--374.

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A. Panconesi and A. Srinivasan. On the complexity of distributed network decomposition. Journal of Algorithms, 20:356-374, 1996.

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