Rank Detection Methods for Sparse Matrices

In today's rapidly changing field of Management Information Systems (MIS) one problem faced by organizations is the consumption of storage capacity due to the growing base of software assets. Research has shown that very few firms effectively monitor program usage. Storage management issues arise due to the fact that many of the programs occupying valuable storage space are used infrequently. In this dissertation, we apply Simon's model of information usage in order to model the dynamic behavior of program usage. This methodology enables organizations to identify the changing usage frequencies of software assets. We propose a classification scheme which MIS personnel can use in order to effectively monitor their program usage tendencies. This classification scheme may then serve as a basis for storage allocation decision-making. Through a study of the dynamic behavior of programs, we have formulated a minimum cost model for hierarchical storage allocation. We will show the value of incorporating dynamic usage frequencies into algorithms which have traditionally considered only a static view.

Graph Theory Dynamic Storage Allocation is a problem concerned with storing items that each have weight and time restrictions. Approximate algorithms have been constructed through online coloring of interval graphs. We present a generalization that uses online coloring of tolerance graphs. We utilize online-with-representation algorithms on tolerance graphs, which are online algorithms in which the corresponding tolerance representation of a vertex is also presented. We find linear bounds for the online-with-representation chromatic number of various classes of tolerance graphs and apply these results to a generalization of Dynamic Storage Allocation, giving us a polynomial time approximation algorithm with linear performance ratio.

In computer science, dynamic storage allocation refers to the mechanisms for managing primary and secondary storage under a fluctuating demand. In this paper we identify three principal sources of inefficient use of storage: partition fragmentation, checkerboarding and internal fragmentation. The first arises when a set of records, to be stored in a set of independent storage units, cannot be partitioned into subsets whose cumulative sizes are equal to the capacities of the storage units. Checkerboarding refers to the alternating holes and occupied regions of a storage device which occur as records come and go unpredictably. Finally, internal fragmentation occurs in systems that allocate storage only in certain prescribed amounts, e.g. the nearest power of two no smaller than the amount requested. In connection with these types of fragmentation, a number of algorithm and storage design questions arise. Our basic goal is to review analyses of combinatorial models of these problems. The major theme of the results is the characterization of approximation algorithms in terms of asymptotic bounds on their performance relative to optimization rules. Our presentation is distinguished by its attempt to bring together for the first time many disparate research efforts in dynamic storage allocation, classifying them by the types of fragmentation studied.

Dynamic storage allocation with limited compaction - complexity and some practical implications

Combinatorial Aspects of Interval Orders and Interval Graphs

: This exploratory development program was originally aimed at developing a computer with features to specifically support the JOVIAL (J73) programming language with considerations to Ada. Later, the program was redirected to modify the instruction set architecture (ISA) to more fully support Ada and increase performance. The new ISA supports most of the standard functions found in most ISA, but gives additional supports in: the Ada package concept, processing arrays nd records, unconstrained arrays, dynamic storage allocation, detecting dangling references, detecting undefined variables, Ada-like exception handling, case instructions, for-loop instructions, Ada-like parameter passing, Ada-like tasking instructions and IEEE-standard floating point data types. Keywords: High level language Ada machine, Semantic gap reduction; Language-directed architecture; Non-Von Neumann architecture; Object oriented architecture; Capability based addressing.

Memory management has become an important part in developing real-time and embedded applications. The conventional dynamic storage allocation (DSA) algorithms have been considered inappropriate for real-time applications due to the unbounded response time and fragmentation problem. There are some new allocators designed to meet the requirements nowadays. Two-Level Segregated Fit memory allocator (TLSF) was proposed and widely used in the Real-Time Operating Systems (RTOS) like RTLinux. It has a bounded response time and quite good performance. However, there are still some problems with this algorithm and it could be improved. Here we discuss some improvements of the TLSF algorithm. Experiments show it has low fragmentation and faster response time.

Particularly in scientific community the size of digital data to be stored is ramping up. For those application characterized by very dynamic workloads is difficult to estimate the real size of storage to be allocated and avoid over-provisioning, also in extremely elastic environments as cloud computing. DAViS (Dynamic Allocation of Virtual Storage) is a prototype of a system for dynamically providing virtual block storage to Virtual Machines (VMs), optimizing the physical resources utilization, through dynamic and autonomous resizing of the storage.

Programming is the process of developing a scheme for solving a problem using a computer. The programmer's task is to minimize the cost of achieving a solution. This cost involves the interrelated factors of planning, coding, debugging, storage space, and computation time. The storage allocation problem is the subtask of assigning the space-taking objects (programs and data) to the available storage devices (core, drum, disc and magnetic tape).

We developed a parallel algorithm to improve the cache behavior and overall performance for multiplication of sparse matrices with sparse vectors (SpMSpV), an operation used increasingly in large graph analytics, particularly dynamic graphs in social networks and homeland security applications. The proposed algorithm builds upon the two-phase approach of partitioning the multiplication into a scaling phase and an aggregation phase, to achieve more cache-friendly access patterns individually in each phase [6], [3]. However, to handle dynamic graphs and achieve better load balancing for parallel implementation, we use a combination of private and shared bins, with synchronized access to shared bins to exchange the product terms between the two phases. The new algorithm accumulates product terms in private bins for each thread. The algorithm then performs a bulk transfer between a private bin and a shared bin, when the private bin becomes full. Then results are aggregated from the shared bins. In addition, we employ heuristics to decide the best algorithm for SpMSpV based on the number of nonzeros involved in the operation. When the number of nonzeros is large, it may be better to perform the operation as SpMV (sparse matrix times dense vector) despite the added conversion cost. Also, if the number of nonzeros is low it is advantageous to use a simplified algorithm. We compared our algorithm with existing algorithms for SpMSpV, and our evaluation shows that execution time is reduced by several times when large graphs are considered.

We study the semantic meaning of block structure using game semantics and introduce the notion of block-innocent strategies, which turns out to characterise call-by-value computation with block-allocated storage through soundness, finitary definability and universality results. This puts us in a good position to conduct a comparative study of purely functional computation, computation with block storage and dynamic memory allocation respectively. For example, we show that dynamic variable allocation can be replaced with block-allocated variables exactly when the term involved (open or closed) is of base type and that block-allocated storage can be replaced with purely functional computation when types of order two are involved. To illustrate the restrictive nature of block structure further, we prove a decidability result for a finitary fragment of call-by-value Idealized Algol for which it is known that allowing for dynamic memory allocation leads to undecidability.

Heterogeneous sparse matrix–vector multiplication via compressed sparse row format

This paper studies the solution of the linear least squares problem for a large and sparse m by n matrix A with $m \geq n$ by $QR$ factorization of A and transformation of the right-hand side vector b to $Q^T b$. A multifrontal-based method for computing $Q^T b$ using Householder factorization is presented. A theoretical operation count for the K by K unbordered grid model problem and problems defined on graphs with $\sqrt n $-separators shows that the proposed method requires $O( N_R )$ storage and multiplications to compute $Q^T b$, where $N_R = O( n \log n )$ is the number of nonzeros of the upper triangular factor R of A. In order to introduce BLAS-2 operations, Schreiber and Van Loan's storage-efficient WY representation [SIAM J. Sci. Stat. Comput., 10 (1989), pp. 53–57] is applied for the orthogonal factor $Q_i $ of each frontal matrix $F_i $. If this technique is used, the bound on storage increases to $O( ( n \log n )^2 )$. Some numerical results for the grid model problems as well as Harwell–Boeing problems are provided.

We investigate the scalability of the hypergraph-based sparse matrix partitioning methods with respect to the increasing sizes of matrices and number of nonzeros. We propose a method to rowwise partition the matrices that correspond to the discretization of two-dimensional domains with the five-point stencil. The proposed method obtains perfect load balance and achieves very good total communication volume. We investigate the behaviour of the hypergraph-based rowwise partitioning method with respect to the proposed method, in an attempt to understand how scalable the former method is. In another set of experiments, we work on general sparse matrices under different scenarios to understand the scalability of various hypergraph-based one- and two-dimensional matrix partitioning methods.

Some programming languages and computer systems use dynamic memory allocation with garbage collection. It would be useful to understand how the utilization of memory depends on the stochastic parameters describing the size and life distributions of the cells. We consider a class of dynamic storage allocation systems which use a first-fit strategy to allocate cells and perform noncompacting garbage collections to recover free memory space when memory becomes fully occupied. A formula is derived for the expected number of holes (available cells) in memory immediately following a garbage collection which specializes to an analogue of Knuth's 'Fifty Percent' rule for nongarbage-collection systems. Simulations confirm the rule for exponentially distributed cell lifetimes. Other lifetime distributions are discussed. The memory-size requirements for noncompacting garbage collection are also analyzed.