It has since been used in a near-linear time algorithm for finding minimum cuts, as well as faster cut and flow algorithms. Our approach gives a general paradigm with potential applications to any packing problem. Our cut-approximation algorithms extend unchanged to weighted graphs while our weighted-graph flow algorithms are somewhat slower. We present fast randomized (Monte Carlo and Las Vegas) algorithms for approximating and exactly finding minimum cuts and maximum flows in unweighted, undirected graphs. This makes sampling effective for problems involving cuts in graphs. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph’s edges will accurately approximate the value of all cuts in the original graph with high probability. We use random sampling as a tool for solving undirected graph problems. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class - an object receives a probability essentially proportional to an exponential of its size.Īs demonstrated here, the resulting algorithms based on real-arithmetic operations often operate in linear time. This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. We recall the main developments in non-uniform random variate generation.
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