We are interested in the quantitative analysis of compaction ratio for two classical families trees: recursive trees and plane binary increasing trees. These typical representatives tree models with a small depth. Once size n is compacted by keeping only one occurrence all fringe subtrees appearing resulting graph contains nodes. This result must be compared to results simply generated trees, w...

In functional languages, iterative operations on data collections are naturally expressed using recursive functions on recursive data structures. In this paper, we present a method to extract data parallelism from recursive functions and generate data parallel programs. As the parallel model for object programs, we use polytypic parallel skeletons. This model can express data parallel operation...

Decision trees in which numeric attributes are split several ways are more comprehensible than the usual binary trees because attributes rarely appear more than once in any path from root to leaf. There are efficient algorithms for finding the optimal multiway split for a numeric attribute, given the number of intervals in which it is to be divided. The problem we tackle is how to choose this n...

In a recent paper Broutin and Devroye (2005) have studied the height of a class of edge-weighted random trees. This is a class of trees growing in continuous time which includes many well known trees as examples. In this paper we derive a limit theorem for the internal path length for this class of trees. The application of this limit theorem to concrete examples depends upon the possibility to...

Abstract The article proposes an addition to the tunnel parsing algorithm that enables it parse grammars having countable repetitions and configurations of grammar elements generating empty words without refactoring grammar. equivalency trees built by use ambiguous is discussed. class ε-ambiguous defined as a subclass relative these trees. ε-deterministic are then grammars. A technique for line...

We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn − E[Zn], n ≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by...

Exponential tail bounds are derived for solutions of max-recursive equations and for maxrecursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise in the worst case analysis of divide and conquer algorithms, in parallel search algorithms or in the height of random tree models. For the proof we de...

The metric dimension of a graph G is the minimal size subset R vertices that, upon reporting their distance from distinguished (source) vertex v?, enable unique identification source v? among all possible G. In this paper we show Law Large Numbers (LLN) for some classes trees: critical Galton–Watson trees conditioned to have n, and growing general linear preferential attachment trees. former cl...

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. ...

This paper describes a denotational approach to the Petri net semantics of recursive expressions. A domain of nets is identified such that the solution of a given recursive equation can be found by fixpoint approximation from some suitable starting point. In turn, a suitable starting point can be found by fixpoint approximation on a derived domain of sets of trees. The paper explains the theory...