32899707
Computing the normal forms of matrices depending on parameters
We consider in this paper an algorithm for the exact computation of the Frobenius, Jordan and Arnold's form of matrices depending holomorphically on parameters. The problem originates from the problem of formal resolution of a first order system of differential equations depending on parameter. We have implemented this algorithm in Macsyma.
5887540
An Algorithm for Computing a New Normal Form for Dynamical Systems
We propose in this paper a new normal form for dynamical systems or vector fields which improves the classical normal forms in the sense that it is a further reduction of the classical normal forms. We give an algorithm for an effective computation of these normal forms. Our approach is rational in the sense that if the coefficients of the system are in a field K(which, in practice, is Q, R), so is the normal form and all computations are done inK . As a particular case, if the matrix of the linear part is a companion matrix then we reduce the dynamical system to a single differential equation. Our method is applicable for both the nilpotent and the non-nilpotent cases. We have implemented our algorithm in Maple V and obtained many examples of the further reduced normal forms up to some finite order.
17810541
An adaptive locality-conscious process scheduler for embedded systems
A critical component of a real-time operating system (RTOS) is its process scheduler. While the prior research on process scheduling focuses mostly on meeting hard/soft deadlines, preemption and priory assignment related issues, problems arise from existence of cache memories are largely ignored. Focusing on data accesses and a cache based embedded system, this paper proposes an adaptive locality-conscious process scheduling algorithm. The main goal of the proposed algorithm is to exploit (reuse) the contents of the on-chip cache memory to the highest extent possible. The algorithm tries to achieve its goal by determining the order in which the processes get scheduled such that the successively-executing processes share a large number of data elements. We implemented our scheduler within a customized simulation platform and simulated it using a set of benchmark codes. Our experimental results reveal that the proposed scheduling algorithm is very successful in practice, and reduces process completion times significantly for both rate-monotonic scheduling (RMS) and earliest-deadline-first scheduling (EDF). We also explain how process code transformations can be used for increasing the savings achieved by the locality-conscious scheduler, and show how the proposed approach operates with a base scheduler such as RMS and EDF.
206843939
The Quickest Path Problem in Distributed Computing Systems
Let N=(V, A, C, L) be an input network with node set V, arc set A, positive arc capacity function C, and nonnegative arc lead time function L. The quickest path problem is to find a path in N to transmit a given amount of data such that the transmission time is minimized. In this paper, distributed algorithms are developed for the quickest path problem in an asynchronous communication network. For the one-source quickest path problem, we present two algorithms that require O(rn2) messages, O(rn2) time, and O(rmn) messages, O(rn) time, respectively, where m=¦A¦, n=¦V ¦, and r is the number of distinct capacity values of N. For the all-pairs quickest path problem, we present an algorithm that requires O(mn) messages and O(m) time.
13201367
Generalized Diameters of the Mesh of Trees
Abstract
The mesh of trees, which owns two favorable properties, small diameter and large bisection,
is known as the fastest network when considered in terms of speed. In this paper we show that
the wide diameter, fault diameter and Rabin number, which are three generalizations of diameter,
of a two-dimensional 2n×2n mesh of trees are equal to 5n + 1.


316842
Cycles in 4-connected planar graphs
Let G be a 4-connected planar graph on n vertices. Previous results show that G contains a cycle of length k for each k ∈ {n, n - 1,n - 2, n - 3} with k ≥ 3. These results are proved using the "Tutte path" technique, and this technique alone cannot be used to obtain further results in this direction. One approach to obtain further results is to combine Tutte paths and contractible edges. In this paper, we demonstrate this approach by showing that G also has a cycle of length k for each k ∈ {n - 4, n - 5, n - 6} with k ≥ 3. This work was partially motivated by an old conjecture of Malkevitch.
2371887
Locality-conscious process scheduling in embedded systems
In many embedded systems, the existence of a data cache might influence the effectiveness of process scheduling policy significantly. Consequently, a scheduling policy that takes inter-process data reuse into account might result in large performance benefits. In this paper, we focus on array-intensive embedded applications and present a locality-conscious scheduling strategy where we first evaluate the potential data reuse between processes, and then, using the results of this evaluation, select an order for process executions. We also show how process codes can be transformed by an optimizing compiler for increasing inter-process data reuse, thereby making locality-conscious scheduling more effective. Our experimental results obtained using two large, multi-process application codes indicate significant runtime benefits.