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This work earned its authors the Fulkerson Prize.


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Subsequent authors improved the running time of this method by providing more quickly mixing Markov chains for the same problem. From Wikipedia, the free encyclopedia.

Newton polytopes, monomial maps, and power series — phcpy documentation

The algorithm combines two ideas: By using a Markov chain Monte Carlo MCMC method, it is possible to generate points that are nearly uniformly randomly distributed within a given convex body. By using the theory of rapidly mixing Markov chains , they show that it takes a polynomial time for the random walk to settle down to being a nearly uniform distribution.

The basic idea is to generate random points within the outer of the two bodies, and to count how often those points are also within the inner body.


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    Polynomial Approximation on Polytopes

    Economic literature: papers , articles , software , chapters , books. Random walk in a simplex and quadratic optimization over convex polytopes. In this paper we develop probabilistic arguments for justifying thequality of an approximate solution for global quadratic minimization problem, obtained as a best point among all points of a uniform grid inside a polyhedral feasible set.