The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Fast probabilistic algorithms for hamiltonian circuits and matchings
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The theory of random graphs with applications to the probabilistic analysis of optimization algorithms.
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In the past, most algorithmic analysis has centered On the determination of the worst case performance. In real world applications, the average performance of an algorithm is of far more interest. In this paper, we use the results of the theory of random graphs to aid in the design and analysis of more efficient graph theoretic optimization algorithms. The results show that the theory of random graphs can be a powerful tool in the analysis of average algorithm performance. The topics covered in this paper include a discussion of one to one shortest path algorithms, minimum spanning tree algorithms, and algorithms for the traveling salesman problem. We conclude with a discussion of areas for future research. The purpose of this paper is to give a flavor of what is possible using the theory of random graphs. Thus the discussion is kept relatively free of mathematical detail.