![algoritma pemrograman parallel graph coloring algoritma pemrograman parallel graph coloring](http://users.oden.utexas.edu/~gopal/software/sparc/html/coarsening.png)
By average case we mean that the inputs are selected randomly from some natural family of distributions parametrized by problem size. We examine here the average-case parallel complexity of graph coloring problems (which are known to be NP-hard in the worst case). T1 - Fast parallel algorithms for coloring random graphs 17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1991 Conference date: 17-06-1991 Through 19-06-1991",
![algoritma pemrograman parallel graph coloring algoritma pemrograman parallel graph coloring](https://piptools.net/wp-content/uploads/2016/12/cmd154.png)
Publisher Copyright: Springer-Verlag Berlin Heidelberg 1992. 3075 (ALCOM), by the Ministry of Industry, Energy and Technology of Greece and by the NSF grant CCR-89-6949. Here the instance is known to h.ave the property we are seeking and *This work was partially supported by the EEC ESPRIT Basic Research Action No. (b) The class of all k-colorable graphs, for k constant and edge probabihty p = f~(~), where each graph is uniformly chosen. If p < O(log n/n) both algorithms have the same performance on a CRCW PRAM. The algorithm of \f inds the same number of colors, uses the same number of processors on a CRCW PRAM and runs in O(log 5 n~ log log n) time for p = ft(log n/n), with probabihty at least 1 - O(1/log n). We consider two families of random graphs: (a) The class G,p of graphs of n vertices where each edge may be independently present with probability p (see \).F or this class of graphs we modify an algorithm of \a nd do a tight analysis, through which we show that our algorithm colors the input with a number of colors at most twice its chromatic number, in parallel time O(log 4 n~ log log n) by using O(n2p) processors for p = ft((log (a) n)2/log(2) n), on a CRCW PRAM, with probability at least 1 - n -d (d > 1). Note = "Funding Information: We examine here the average-case parallel complexity of graph coloring problems (which are known to be NP-hard in the worst case).