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Graph Coloring on Coarse Grained Multicomputers
, 2002
"... We present an efficient and scalable Coarse Grained Multicomputer (CGM) coloring algorithm that colors a graph G with at most D+ 1 colors where D is the maximum degree in G. This algorithm is given in two variants: randomized and deterministic. We show that on a pprocessor CGM model the proposed al ..."
Abstract

Cited by 6 (1 self)
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We present an efficient and scalable Coarse Grained Multicomputer (CGM) coloring algorithm that colors a graph G with at most D+ 1 colors where D is the maximum degree in G. This algorithm is given in two variants: randomized and deterministic. We show that on a pprocessor CGM model the proposed algorithms require a parallel time of O( G p ) and a total work and overall communication cost of O(G). These bounds correspond to the average case for the randomized version and to the worstcase for the deterministic variant. Key words: graph algorithms, parallel algorithms, graph coloring, Coarse Grained Multicomputers 1
Improved EdgeColoring Algorithms for Planar Graphs
 JOURNAL OF ALGORITHMS
, 1996
"... We consider the problem of edgecoloring planar graphs. It is known that a planar graph G with maximum degree \Delta \geq 8 can be colored with \Delta colors. We present two algorithms which find such a coloring when \Delta \geq 9. The first one is a sequential O(n log n) time algorithm. The other o ..."
Abstract

Cited by 4 (1 self)
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We consider the problem of edgecoloring planar graphs. It is known that a planar graph G with maximum degree \Delta \geq 8 can be colored with \Delta colors. We present two algorithms which find such a coloring when \Delta \geq 9. The first one is a sequential O(n log n) time algorithm. The other one is a parallel EREW PRAM algorithm which works in time O(logĀ³ n) and uses O(n) processors.