相关论文: A generating function method for the average-case …

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…

A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…

The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…

We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…

We consider weighted generating functions of trees where the weights are products of functions of the sizes of the subtrees. This work begins with the observation that three different communities, largely independently, found substantially…

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…

This paper shows that decision trees constructed with Classification and Regression Trees (CART) and C4.5 methodology are consistent for regression and classification tasks, even when the number of predictor variables grows…

We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…

Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…

The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…

In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in…

As known, the commonly-utilized ways to determine mean first-passage time $\overline{\mathcal{F}}$ for random walk on networks are mainly based on Laplacian spectra. However, methods of this type can become prohibitively complicated and…

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function.…

In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman…

Motivated by a recently proposed design for a DNA coded randomised algorithm that enables inference of the average generation of a collection of cells descendent from a common progenitor, here we establish strong convergence properties for…

We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…

Additive tree functionals allow to represent the cost of many divide-and-conquer algorithms. We give an invariance principle for such tree functionals for the Catalan model (random tree uniformly distributed among the full binary ordered…

We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph $G=(V,E)$ and a positive semi-definite matrix $\mathbf{A}$ indexed by $E$, a spanning-tree DPP defines a distribution such that we draw…

We consider Monte-Carlo Tree Search (MCTS) applied to Markov Decision Processes (MDPs) and Partially Observable MDPs (POMDPs), and the well-known Upper Confidence bound for Trees (UCT) algorithm. In UCT, a tree with nodes (states) and edges…