RNC Algorithms for the Uniform Generation of Combinatorial Structures

RNC Algorithms for theUniform Generation of Combinatorial

We describe several RNC algorithms for generating graphs and subgraphs uniformly at random. For example, unla-belled undirected graphs are generated in O(lg 3 n) time using O "n 2 lg 3 n processors if their number is known in advance and in O(lg n) time using O "n 2 lg n processors otherwise. In both cases the error probability is the inverse of a polynomial in ". Thus " may be chosen to trade-...

Using the Particle Swarm Optimization Algorithm to Generate the Minimum Test Suite in Covering Array with Uniform Strength

Up to now, several useful algorithms have been proposed to generate covering array, which is one of the branches of combinatorial testing. The main challenge in generating such arrays is generation of the arrays with a minimum number of test cases (for efficiency) at a proper time (for performance), for large systems. Covering array generation strategies are often divided into two general categ...

Eecient and Fast Rnc Algorithms for the Uniform Generation of Unlabelled Graphs

Random Generation of Combinatorial Structures from a Uniform Distribution (Extended Abstract)

The class of problems involving the random generation of combinatorial structures from a uniform distribution is considered. Uniform generation problems are, in computational difficulty, intermediate between classical existence and counting problems. It is shown that exactly uniform generation of 'efficiently verifiable' combinatorial structures is reducible to approximate counting (and hence, ...

RNC-Approximation Algorithms for the Steiner Problem

In this paper we present an RNC-algorithm for nding a minimum spanning tree in a weighted 3-uniform hypergraph, assuming the edge weights are given in unary, and a fully polynomial time randomized approximation scheme if the edge weights are given in binary. From this result we then derive RNC-approximation algorithms for the Steiner problem in networks with approximation ratio (1 +) 5=3 for al...