Decision Tree Search Research Articles

Fuzzy optimal search methods

This paper gives analytical approaches and algorithms for decision tree search techniques. The decision trees are assumed to have a fixed number of stages and predefined possible states at every stage. The costs of traversing the tree are characterized as approximate and defined as fuzzy numbers. Two search methods, each drawing from an existing non-fuzzy search algorithm, are described. The first method is a dynamic programming search, where the principle of optimality with fuzzy costs is addressed. The second method is an A ∗ search for which the notion of a lower bound estimate of costs is utilized to increase the efficiency of the search. Algorithms for each method are included. Theorems and proofs which complete the analytical development of these techniques are also included. Finally, a numerical example illustrating the procedure is given.

Topological Analysis of Multibody Systems for Recursive Dynamics Formulations

Abstract Graph theory is used to characterize the topology of multibody systems for high speed parallel computer dynamic simulation. Decoupled loops are defined for use in the recursive dynamics formulations, wherein Langrange multipliers can be eliminated concurrently within each decoupled loop. A row-scanning process for the nondirected adjacency matrix of a graph is described, to generate an identification array that facilitates compact storage and defines system connectivities. A decision tree search algorithm is employed to generate all spanning trees associated with a closed loop graph. For each spanning tree generated from the decision tree search algorithm, a precedence array is defined. A path matrix for the spanning tree and an outdegree of junction nodes are defined to assist in parallel implementation of recursive dynamics algorithms and are then constructed from the precedence array. Finally, an optimal tree search algorithm that identifies a spanning tree that leads to best solution sequences for parallel implementation of recursive dynamics formulations is presented.

Variable rate speech compression by encoding subsets of the PARCOR coefficients

In LPC analysis, the speech signal is divided into frames each of which is represented by a vector of estimated vocal tract parameters, assumed to be constant throughout the frame. For many sounds, these parameters do not change significantly from one frame to the next, and some of them can often be adequately represented by previously transmitted values. In the LPC coding systems described in this paper, a number of alternative representations are considered for each frame. These representations (vectors) are combinations of PARCOR coefficients from the current frame and from previous frames. Several consecutive frames are analyzed at once, and all the possible sequences of PARCOR coefficient vectors are examined. The sequence which minimizes a preselected cost function is chosen for transmission, resulting in a reduced overall data rate. The examination of all the decision sequences is equivalent to a decision tree search, which is most efficiently accomplished through dynamic programming. Using these techniques, LPC encoded speech at 1200 bits/s is demonstrated to be of quality comparable to a constant rate LPC vocoder at 2400 bits/s.

The Shortest Hamiltonian Chain of a Graph

Given a graph G with weighted links, the problems considered in this paper are the following: (i) Find the shortest possible Hamiltonian chain (HC) of the graph G when the end vertices are not specified. (ii) Find the shortest possible HC of G when the end vertices are specified. Two basic algorithms are given each of which can solve both of the above problems with only slight modification. The first algorithm, A, is based on a decision-tree search with lower bounds used to limit the search. The second algorithm, B, is a fast iterative procedure which is based on simple transformations of the cost matrix of the graph G, ensuring at each step that the relative cost of all Hamiltonian chains stay unchanged. Both algorithms ensure the optimality of the final answer, but whereas the convergence of Algorithm A is self-evident, no proof of convergence has been obtained for Algorithm B. However, tests of Algorithm B (which is both simpler and computationally superior to Algorithm A) on a number of sample problems have not produced any difficulties with convergence. Two examples are given to illustrate the two methods.