Journal ArticleDOI
The greedy coloring is a bad probabilistic algorithm
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It is proved that for each n there is a graph G n such that the chromatic number of G n is at most n e, but the probability that A(G n, p) (1 − ϑ)n log 2 n for a randomly chosen ordering p is O ( n − Δ ).About:
This article is published in Journal of Algorithms.The article was published on 1991-12-01. It has received 57 citations till now. The article focuses on the topics: Greedy coloring & Randomized algorithm.read more
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Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
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Expected complexity of graph partitioning problems
TL;DR: The expected time complexity of two graph partitioning problems: the graph coloring and the cut into equal parts is studied to obtain a sublinear expected time algorithm for k-coloring of k-colorable graphs.
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Graph Coloring with Adaptive Evolutionary Algorithms
TL;DR: The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances and scales up better with the problem size than the other two algorithms.
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Algorithmic theory of random graphs
Alan Frieze,Colin McDiarmid +1 more
TL;DR: There has been increasing interest in using random graphs as models for the average case analysis of graph algorithms, and some of the results are surveyed.
Exploring the k-colorable landscape with Iterated Greedy.
Joseph C. Culberson,Feng Luo +1 more
TL;DR: This work introduces several heuristics for generating new permutations that are fast when implemented and eeective in reducing the coloring number and explores the areas of diiculty in probabilistic graph space under several parameterizations.
References
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Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
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A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
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Universal classes of hash functions
TL;DR: An input independent average linear time algorithm for storage and retrieval on keys that makes a random choice of hash function from a suitable class of hash functions.
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A Fast Monte-Carlo Test for Primality
Robert Solovay,Volker Strassen +1 more
TL;DR: A uniform distribution a from a uniform distribution on the set 1, 2, 3, 4, 5 is a random number and if a and n are relatively prime, compute the residue varepsilon.
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Almost all k -colorable graphs are easy to color
TL;DR: A simple and efficient heuristic algorithm for the graph coloring problem is described and it is shown that for all k ≥ 1, it finds an optimal coloring for almost all k -colorable graphs.