Showing papers on "Las Vegas algorithm published in 2004"
01 Jul 2004
TL;DR: An adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(m log n) queries, which is tight up to a constant factor for classes of non-dense graphs, and a non-adaptive Monte Carlo algorithm that succeeds with probability at least 1–n − − c.
Abstract: We consider the problem of learning a general graph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden graph. This model has been studied for particular classes of graphs by Kucherov and Grebinski [1] and Alon et al.[2], motivated by problems arising in genome sequencing. We give an adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(m log n) queries, which is tight up to a constant factor for classes of non-dense graphs. Allowing randomness, we give a 5-round Las Vegas algorithm using \(O(m {\rm log}n+\sqrt{m}{\rm log}^{2}n)\) queries in expectation. We give a lower bound of Ω((2m/r) r/2) for learning the class of non-uniform hypergraphs of dimension r with m edges. For the class of r-uniform hypergraphs with bounded degree d, where d≤ n 1/( r− − 1)/(2r 1 + 2/( r− − 1)), we give a non-adaptive Monte Carlo algorithm using O(dnlog n) queries, which succeeds with probability at least 1–n − − c, where c is any constant.
55 citations
TL;DR: New, efficient algorithms for computations on separable matrix algebras over infinite fields yield a partial factorization of the minimal polynomial of the generator that is computed, which may reduce the cost of computing simple components of the algebra in some cases.
19 citations
05 Apr 2004
TL;DR: Fleischer, Jung, Mehlhorn (1995) have shown that if a Las Vegas algorithm expects to communicate Ω(n logn) bits, then this can be done with a small number of coin tosses.
Abstract: Two processors receive inputs X and Y respectively. The communication complexity of the function f is the number of bits (as a function of the input size) that the processors have to exchange to compute f(X,Y) for worst case inputs X and Y. The List-Non-Disjointness problem (X=(x 1,...,x n ), Y=(y 1,...,y n ), \(x^{j},y^{j}\in {\rm Z}^{n}_{2}\), to decide whether \(\exists_{j}x^{j}=y^{j}\)) exhibits maximal discrepancy between deterministic n 2 and Las Vegas (Θ(n)) communication complexity. Fleischer, Jung, Mehlhorn (1995) have shown that if a Las Vegas algorithm expects to communicate Ω(n logn) bits, then this can be done with a small number of coin tosses.