The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between groups. We present a simple, linear-tim...

We show that likelihood judgments are biased toward an ignorance-prior probability that assigns equal credence to each mutually exclusive event considered by the judge. The value of the ignorance prior depends crucially on how the set of possibilities (i.e., the state space) is subjectively partitioned by the judge. For instance, asking "what is the probability that Sunday will be hotter than a...

For a graph G = (V,E) of even order, a partition (V1, V2) of the vertices is said to be perfectly balanced if |V1| = |V2| and the numbers of edges in the subgraphs induced by V1 and V2 are equal. For a base graph H define a random graph G(H, p) by turning every non-edge of H into an edge and every edge of H into a nonedge independently with probability p. We show that for any constant ǫ there i...

| The paper compares partition testing and random testing on the assumption that program failure rates are not known with certainty before testing and are therefore modeled by random variables. It is shown that under uncertainty, partition testing compares more favorably to random testing than suggested by prior investigations concerning the deterministic case: the restriction to failure rates ...

Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P , then we call M a partition of P . Let K denote the set of probability vectors on S. To every partition M of P we can associate a transition probability function PM on K defined in such a way that if p ∈ K and M ...

This paper compares partition testing and random testing on the assumption that program failure rates are not known with certainty before testing and are, therefore, modeled by random variables. It is shown that under uncertainty, partition testing compares more favorably to random testing than suggested by prior investigations concerning the deterministic case: The restriction to failure rates...

We study the asymptotic behavior of the largest part size of a plane partition ω of the positive integer n, assuming that ω is chosen uniformly at random from the set of all such partitions. We prove that this characteristic, appropriately normalized, tends weakly, as n → ∞, to a random variable having an extreme value probability distribution with distribution function, equal to e−e −z ,−∞ < z...