Call Control in Rings

The call control problem is an important optimization problem encountered in the design and operation of communication networks. The goal of the call control problem in rings is to compute, for a given ring network with edge capacities and a set of paths in the ring, a maximum cardinality subset of the paths such that no edge capacity is violated. We give a polynomial-time algorithm to solve the problem optimally. The algorithm is based on a decision procedure that checks whether a solution with at least k paths exists, which is in turn implemented by an iterative greedy approach operating in rounds. We show that the algorithm can be implemented efficiently and, as a by-product, obtain a linear-time algorithm to solve the problem in chains optimally. For the weighted version of call control in rings, where each path is associated with a weight and the goal is to maximize the total weight of the paths in the solution, we present a simple 2-approximation algorithm and a polynomial-time approximation scheme. While the complexity of the weighted version remains open, we show that it is at least as hard as the bipartite exact matching problem, which has not been resolved to be in P or NP-hard. This latter result follows from recent work by Hochbaum and Levi

SPRING BASED ON FLAT PERMANENT MAGNETS: DESIGN, ANALYSIS AND USE IN VARIABLE STIFFNESS ACTUATOR

Modern robot applications benefit from including variable stiffness actuators (VSA) in the kinematic chain. In this paper, we focus on VSA utilizing a magnetic spring made of two coaxial rings divided into alternately magnetized sections. The torque generated between the rings is opposite to the angular deflection from equilibrium and its value increases as the deflection grows – within a specific range of angles that we call a stable range. Beyond the stable range, the spring exhibits negative stiffness what causes problems with prediction and control. In order to avoid it, it is convenient to operate within a narrower range of angles that we call a safe range. The magnetic springs proposed so far utilize few pairs of arc magnets, and their safe ranges are significantly smaller than the stable ones. In order to broaden the safe range, we propose a different design of the magnetic spring, which is composed of flat magnets, as well as a new arrangement of VSA (called ATTRACTOR) utilizing the proposed spring. Correctness and usability of the concept are verified in FEM analyses and experiments performed on constructed VSA, which led to formulating models of the magnetic spring. The results show that choosing flat magnets over arc ones enables shaping spring characteristics in a way that broadens the safe range. An additional benefit is lowered cost, and the main disadvantage is a reduced maximal torque that the spring is capable of transmitting. The whole VSA can be perceived as promising construction for further development, miniaturization and possible application in modern robotic mechanisms

Multiclass scheduling algorithms for the DAVID metro network

Abstract—The data and voice integration over dense wavelength-division-multiplexing (DAVID) project proposes a metro network architecture based on several wavelength-division-multiplexing (WDM) rings interconnected via a bufferless optical switch called Hub. The Hub provides a programmable interconnection among rings on the basis of the outcome of a scheduling algorithm. Nodes connected to rings groom traffic from Internet protocol routers and Ethernet switches and share ring resources. In this paper, we address the problem of designing efficient centralized scheduling algorithms for supporting multiclass traffic services in the DAVID metro network. Two traffic classes are considered: a best-effort class, and a high-priority class with bandwidth guarantees. We define the multiclass scheduling problem at the Hub considering two different node architectures: a simpler one that relies on a complete separation between transmission and reception resources (i.e., WDM channels) and a more complex one in which nodes fully share transmission and reception channels using an erasure stage to drop received packets, thereby allowing wavelength reuse. We propose both optimum and heuristic solutions, and evaluate their performance by simulation, showing that heuristic solutions exhibit a behavior very close to the optimum solution. Index Terms—Data and voice integration over dense wavelength-division multiplexing (DAVID), metropolitan area network, multiclass scheduling, optical ring, wavelength-division multiplexing (WDM). I

Spartan Daily, November 5, 1979

Volume 73, Issue 44https://scholarworks.sjsu.edu/spartandaily/6542/thumbnail.jp

Homalg: A meta-package for homological algebra

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.Comment: clarified some points, added references and more interesting example

Computing diagonal form and Jacobson normal form of a matrix using Gr\"obner bases

In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gr\"obner bases. This can be viewed as the pre-processing for the computation of Jacobson normal form and also used for the computation of Smith normal form in the commutative case. We propose a general framework for handling, among other, operator algebras with rational coefficients. We employ special "polynomial" strategy in Ore localizations of non-commutative $G$-algebras and show its merits. In particular, for a given matrix $M$ we provide an algorithm to compute $U,V$ and $D$ with fraction-free entries such that $UMV=D$ holds. The polynomial approach allows one to obtain more precise information, than the rational one e. g. about singularities of the system. Our implementation of polynomial strategy shows very impressive performance, compared with methods, which directly use fractions. In particular, we experience quite moderate swell of coefficients and obtain uncomplicated transformation matrices. This shows that this method is well suitable for solving nontrivial practical problems. We present an implementation of algorithms in SINGULAR:PLURAL and compare it with other available systems. We leave questions on the algorithmic complexity of this algorithm open, but we stress the practical applicability of the proposed method to a bigger class of non-commutative algebras