A deterministic parallel algorithm for parallel tree contraction is presented in this paper. The algorithm takes T time and uses (P processors, where n the number of vertices in a tree using an Exclusive Read and Exclusive Write (EREW) Parallel Random Access Machine (PRAM). This algorithm improves the results of Miller and who use the CRCW randomized PRAM model to get the same complexity and pr...

An edge reconnection is an operation on a path of three consecutive vertices (a, b, c) of a chain or tree linkage; refer to Figure 1. If it is possible to fold the linkage, preserving edge lengths and avoiding self-intersection, to bring the two incident edges ab and bc into coincidence, then the edge reconnection breaks the connection between the edges at b, splits b into two vertices b1 and b...

Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are natural analogues of the maximal nilpotent Lie subalgebras of finite-dimensional simple Lie algebras. In this paper, we use Hodge Laplacian to study the coho...

Voting trees describe an iterative procedure for selecting a single vertex from a tournament. It has long been known that there is no voting tree that always singles out a vertex with maximum degree. In this paper, we study the power of voting trees in approximating the maximum degree. We give upper and lower bounds on the worst-case ratio between the degree of the vertex chosen by a tree and t...

Motivated by a desire to assess the prosody of foreign language learners, this study demonstrates the benefit of highlevel syntactic information in automatically deciding where phrase breaks and pitch accents should go in text. The connection between syntax and prosody is well-established, and naturally lends itself to tree-based probabilistic models. With automatically-derived parse trees pair...

We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for the special case of the tree being a star, we show that the problem is np-hard. For the special case of the tree being a path, this problem is known to be pol...

We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root ...

Coquidt, J.-L., M. Dauchet, R. Gilleron and S. VBgviilgyi, Bottom-up tree pushdown automata: classification and connection with rewrite systems, Theoretical Computer Science 127 (1994) 69-98. We define different types of bottom-up tree pushdown automata and study their connections with rewrite systems. Along this line of research we complete and generalize the results of Gallier, Book and Salom...

Many distributed multimedia applications involve data delivery from a source to multiple destinations, the participating nodes forming a multicast group. In the naive solution, a separate connection can be established from the source to other group nodes. However, better solutions have been devised. A tree can be established for each source with the participants as the leaf nodes or just have o...