Supporting Data Structures Research Articles

Linear Time Universal Coding and Time Reversal of Tree Sources Via FSM Closure

Tree models are efficient parametrizations of finite-memory processes, offering potentially significant model cost savings. The information theory literature has focused mostly on redundancy aspects of the universal estimation and coding of these models. In this paper, we investigate representations and supporting data structures for finite-memory processes, as well as the major impact these structures have on the universal algorithms in which they are used. We first generalize the class of tree models, and then define and investigate the properties of the finite-state machine (FSM) closure of a tree, which is the smallest FSM that generates all the processes generated by the tree. The interaction between FSM closures, generalized context trees (GCTs), and classical data structures such as compact suffix trees brings together the information-theoretic and the computational aspects, leading to the first algorithm for linear time encoding/decoding of a lossless twice-universal code in the class of three models. The implemented code is a two-pass version of Context. The corresponding optimal context selection rule and context transitions use tools similar to those employed in efficient implementation of the popular Burrows-Wheeler transform (BWT), yielding similar computational complexities. We also present a reversible transform that displays the same "context deinterleaving" feature as the BWT but is naturally based on an optimal context tree. FSM closures are also applied to an investigation of the effect of time reversal on tree models, motivated in part by the following question: When compressing a data sequence using a universal scheme in the class of tree models, can it make a difference whether we read the sequence from left to right or from right to left? Given a tree model of a process, we show constructively that the number of states in the tree model corresponding to the reversed process might be, in the extreme case, quadratic in the number of states of the original tree. This result answers the above motivating question in the affirmative.

Some aspects of adaptive grid technology related to boundary and interior layers

We consider the use of adaptive mesh strategies for solution of problems exhibiting boundary and interior layer solutions. As the presence of these layer structures suggests, reliable and accurate solution of this class of problems using finite difference, finite volume or finite element schemes requires grading the mesh into the layers and due attention to the associated algorithms. When the nature and structure of the layer is known, mesh grading can be achieved during the grid generation by specifying an appropriate grading function. However, in many applications the location and nature of the layer behavior is not known in advance. Consequently, adaptive mesh techniques that employ feedback from intermediate grid solutions are an appealing approach. In this paper, we provide a brief overview of the main adaptive grid strategies in the context of problems with layers. Associated error indicators that guide the refinement feedback control/grid optimization process are also covered and there is a brief commentary on the supporting data structure requirements. Some current issues concerning the use of stabilization in conjunction with adaptive mesh refinement (AMR), the question of “pollution effects” in computation of local error indicators, the influence of nonlinearities and the design of meshes for targeted optimization of specific quantities are considered. The application of AMR for layer problems is illustrated by means of case studies from semiconductor device transport (drift diffusion), nonlinear reaction–diffusion, layers due to surface capillary effects, and shockwaves in compressible gas dynamics.

Categorical database generalization

This paper focuses on the issues of categorical database generalization and emphasizes the roles of supporting data model, integrated data model, spatial analysis and semantic analysis in database generalization. The framework contents of categorical database generalization transformation are defined. This paper presents an integrated spatial supporting data structure, a semantic supporting model and similarity model for the categorical database generalization. The concept of transformation unit is proposed in generalization.

Template meta-programming for Haskell

We propose a new extension to the purely functional programming language Haskell that supports compile-time meta-programming . The purpose of the system is to support the algorithmic construction of programs at compile-time.The ability to generate code at compile time allows the programmer to implement such features as polytypic programs, macro-like expansion, user directed optimization (such as inlining), and the generation of supporting data structures and functions from existing data structures and functions.Our design is being implemented in the Glasgow Haskell Compiler, ghc.

3-D tracking and motion estimation using hierarchical Kalman filter

The authors present a novel approach to the problem of tracking and reconstructing articulated objects in 3-D space. The newly conceived computational process and its supporting data structure, the hierarchical Kalman filter (HKF) and the adaptive hierarchical structure (AHS), allow the problem to be treated in a single, unified framework. There are three novelties in the authors' formulation: reducing the 3-D tracking problem to 2-D tracking; incorporating the kinematic and the dynamic properties of object; and tracking nonrigid objects. To demonstrate the appropriateness of the proposed method, the authors present some of the experimental results on both synthetic and real images.

Supporting dynamic data structures on distributed-memory machines

Compiling for distributed-memory machines has been a very active research area in recent years. Much of this work has concentrated on programs that use arrays as their primary data structures. To date, little work has been done to address the problem of supporting programs that use pointer-based dynamic data structures. The techniques developed for supporting SPMD execution of array-based programs rely on the fact that arrays are statically defined and directly addressable. Recursive data structures do not have these properties, so new techniques must be developed. In this article, we describe an execution model for supporting programs that use pointer-based dynamic data structures. This model uses a simple mechanism for migrating a thread of control based on the layout of heap-allocated data and introduces parallelism using a technique based on futures and lazy task creation. We intend to exploit this execution model using compiler analyses and automatic parallelization techniques. We have implemented a prototype system, which we callOlden, that runs on the Intel iPSC/860 and the Thinking Machines CM-5. We discuss our implementation and report on experiments with five benchmarks.

Acceleration of the LBG algorithm

A concentric spherical search technique is proposed to speed up the clustering process in VQ design. A linear data structure is incorporated into the LBG algorithm to keep and update the information about the proximity among the codewords. This proximity information can significantly reduce the number of candidate codewords to be the closest to a given training vector. An improved k-means type VQ design algorithm is proposed based on the new search technique and the supporting data structure. The new algorithm is simple to implement, valid for general error metric, and demonstrated by present experiments to be considerably faster than previous algorithms. >

Supporting shared data structures on distributed memory architectures

Programming nonshared memory systems is more difficult than programming shared memory systems, since there is no support for shared data structures. Current programming languages for distributed memory architectures force the user to decompose all data structures into separate pieces, with each piece “owned” by one of the processors in the machine, and with all communication explicitly specified by low-level message-passing primitives. This paper presents a new programming environment for distributed memory architectures, providing a global name space and allowing direct access to remote parts of data values. We describe the analysis and program transformations required to implement this environment, and present the efficiency of the resulting code on the NCUBE/7 and IPSC/2 hypercubes.

Divide-and-conquer in planar geometry

In the last few years line-sweep has become the standard method to solve problems that involve computing some property of a set of planar objects. In this paper we argue that at least for sets of orthogonal objects divide-and-conquer is competitive, if a suitable representation of the objects is used. We support this claim by sketching three (new) time-optimal divide-and-conquer algorithms to solve the line segment intersection problem, the measure problem and the contour problem, respectively. It turns out that divide-and-conquer requires simpler supporting data structures while line-sweep permits an easier reduction to a one-dimensional problem.

Software mechanisms for inter-process communication in a class of multiple microprocessor systems

A large class of problems may be solved by small, dedicated systems composed of several independent microcomputers connected in a simple way, without sophisticated interconnection networks. The systems here considered have a rigid, star-like architecture where a number of nodes — System Elements represented by independent microcomputer stations — are connected to a Central System Element via Dual Port Memory (DPM) modules. Each of DPM modules (representing the only non conventional hardware requested to build up the system) is shared between the Central System Element and the ordinary Element connected to the second port. Interaction between processes is on the message basis. Process-owned mailbox concept is adopted all over the system for message dispatching and retrieving. Primitives for message exchange and supporting data structures are presented as well as an operating system kernel allowing more than one process running on each microprocessor.

A computer graphics system for block diagram problems

An experimental on-line network design system is proposed. Called DESIGNPAD, it consists of a small computer with graphic display equipment connected to a time-sharing computer and includes the necessary programming support for the equipment. The system is designed to accept problems covering a broad spectrum of applications in the form of labeled block diagrams. The input/output medium, the man-machine interface, and the supporting data structures, particularly the cellular structure, are discussed.