Rearrangement Algorithm Research Articles

A rearrangement algorithm for switching networks composed of digital symmetrical matrices

The goal of this paper is to study the rearrangeability of switching networks composed of digital symmetrical matrices (DSM networks). We will describe an efficient rearrangement algorithm for rearrangeable DSM networks with O( r 2) time complexity, where r is the number of input (output) switches. We also show that r−1 is an upper bound on the number of existing connections that need to be rearranged in order to realize a connection request.

NEURAL NETWORK FOR CONTROL OF REARRANGEABLE CLOS NETWORKS

Rapid evolution in the field of communication networks requires high speed switching technologies. This involves a high degree of parallelism in switching control and routing performed at the hardware level. The multistage crossbar networks have always been attractive to switch designers. In this paper a neural network approach to controlling a three-stage Clos network in real time is proposed. This controller provides optimal routing of communication traffic requests on a call-by-call basis by rearranging existing connections, with a minimum length of rearrangement sequence so that a new blocked call request can be accommodated. The proposed neural network controller uses Paull's rearrangement algorithm, along with the special (least used) switch selection rule in order to minimize the length of rearrangement sequences. The functional behavior of our model is verified by simulations and it is shown that the convergence time required for finding an optimal solution is constant, regardless of the switching network size. The performance is evaluated for random traffic with various traffic loads. Simulation results show that applying the least used switch selection rule increases the efficiency in switch rearrangements, reducing the network convergence time. The implementation aspects are also discussed to show the feasibility of the proposed approach.

Component Rearrangement on Printed Wiring Boards to Maximize the Fundamental Natural Frequency

A methodology to attain the highest fundamental natural frequency of a printed wiring board by rearranging its components has been developed. A general two-dimensional rearrangement algorithm is developed by which the rearrangement of the component-lead-board (CLB) assemblies is performed automatically for any combination of equal size, unequal size, movable and immovable CLBs. This algorithm is also capable of incorporating two design restrictions: fixed (immovable) components and prohibited (non-swappable) areas. A highly computationally efficient objective function for the evaluation of the automatic rearrangement process is introduced, which is a linear function of the size of the individual CLBs that have been selected for each interchange. The simulated annealing method is adapted to solve the combinatorial rearrangement of the CLBs. Using 61 combinations of boundary conditions, equal and unequal sized CLBs, movable and immovable CLBs, various CLB groupings and sets of material properties, it is found that, when compared to the exact solution obtained by an exhaustive search method, the simulated annealing method obtained the highest fundamental natural frequency within 1 percent for 87 percent of the cases considered, within 0.5 percent for 72 percent of the cases and the true maximum in 43 percent of them. To further increase the fundamental natural frequency the introduction of a single interior point support is analyzed. Depending on the boundary conditions an additional increase in the maximum fundamental natural frequency of 44 to 198 percent can be obtained.

Channel reassignment in TDMA systems: single-carrier transmitting, multiple-carrier hop receiving

Channel reassignment schemes are described for a time-division multiple-access (TDMA) system where a single carrier is available on the transmitting side (Tx-SC), while multiple-carriers are hopped on the receiving side (Rx-MCH). The Tx-SC/Rs-MCH TDMA system configuration is presented as being logically equivalent to a three-stage switching network. This equivalence means that rearrangement algorithms for three-stage switching networks proposed to date can be applied to channel reassignment in the Tx-SC/Rx-MCH system. The maximum number of channels that must be reassigned is shown to be M-1, where M is the number of simultaneous carriers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Asynchronous control algorithms for increasing the efficiency of three-stage connecting networks for multipoint services

A study is made of the problem of designing low complexity control algorithms for controlling three-stage connecting networks with the objective of improving system performance. The chosen approach is based on the theory of connecting networks and makes use of rearrangement algorithms. These algorithms are applicable to a number of environments, including multipoint connections, time plan modifications in satellite systems, and real-time routing. The main feature of the algorithms is an asynchronous mode of operation for modifying the system switching configurations. A theoretical framework has been developed for defining the conditions that must hold for the asynchronous rearrangements to work. A quantitative evaluation of these algorithms obtained with a computer simulation program is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Demand assignment in the ACTS LBR system

The advanced communications technology satellite (ACTS) is an experimental communications satellite being developed by NASA's Lewis Research Center. Low burst rate (LBR) traffic stations will access the ACTS multibeam communications package (MCP) through two hopping beams that can be directed at certain cities and areas in the continental United States. An onboard baseband processor (BBP) demodulates uplink traffic received via two up-link (30 GHz) hopping beams, switches the traffic between uplink and downlink beams at baseband, and then remodulates the traffic for retransmission at 20 GHz via two downlink hopping beams. This study concentrates on the demand assigned operation of the ACTS LBR system where the onboard switch is remote from both the traffic stations and the centralized master control station (MCS). Network control uses inbound and outbound orderwire channels and a BBP control channel thereby allowing the MCS to coordinate assignment of individual 64-kb/s channels in the spacecraft. Models are developed to simulate the dynamics of the demand assignment process in order to verify call blocking behavior, to predict control channel loads, and to evaluate alternative algorithms for burst time plan rearrangement that becomes necessary to minimize blocking under conditions of high-traffic intensity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A rearrangement algorithm for three‐stage switching networks

AbstractIn the three‐stage rearrangeable switch‐ing network, an internal blocking can occur. However, such a blocking can be eliminated by rearranging the already set‐up paths, and thus the network can satisfy any connection requirement. To eliminate this internal blocking, a successive rearrangement of more than one already set‐up path is required. The sequence of the paths to be rearranged can clearly be represented by extending the notion of the connection chain introduced by Gotoh. This paper presents a sufficient condition for the Internal blocking to be eliminated by the rearrangement in the extended connection chain, which is a basis for the rearrangement algorithm. It is also verified that the rearrangement algorithm proposed by Gotoh satisfies the sufficient condition. Based on these results, a connection chain is shown in which the internal blocking can be eliminated by the rearrangement. The algorithm to search for the connection chain and to perform the rearrangement is presented. Compared with past methods, in the proposed method, a fewer number of paths is distorted. The usefulness of the method is examined by a simulation.

A Two-Stage Rearrangeable Broadcast Switching Network

A new rearrangeable broadcast switching network has been invented. In its simplest form, the network has two stages. For larger networks, the switches in each stage can be replaced with two-stage networks to reduce crosspoint cost. The invention is based on an innovative approach of connecting each inlet channel to a multiplicity of first-stage switches according to a predetermined connection pattern. The network grows easily and has simple path hunt and rearrangement algorithms. It provides a general solution for any nonblocking broadcast switching application. Fewer crosspoints are required than in any other known two- or three-stage rearrangeable broadcast network. The connection arrangement exemplifies a topic heretofore unaddressed in combinatorial theory.

Average and worst-case performance of Paull’s algorithms for rearranging threestage connection networks

The average and worstcase performance of four Paull’s algorithms for rearranging threestage connection networks are analyzed from a reswitching number point of view. It is shown that all of the approximation algorithms behave very poorly in the most unfavorable states of the networks. However, regarding the expectation of the number of reswitchings in the thermodynamic limit, it is shown, following Bonomi et al.,that all the algorithms are probabilistically good in the sense that they almost always generate solutions which are close to the optimal ones. Finally, it is pointed out that a refinement according to which reswitchings are confined to the least loaded switches does not improve the worstcase performance of Paull’s rearrangement algorithms.

Application of Some Rearrangement Algorithms to a T-S-T Network

The degree to which rearrangement reduces blocking, and its cost in time and complexity, depend on the algorithm used. Here we apply two algorithms to a range of time-space-time networks and compare the results obtained with those produced by Akiyama. We note that in one of these algorithms some states can occur which make effective rearrangement impossible, a condition which does not have a parallel in space division networks.

Backtracking with multi-level dynamic search rearrangement

The order in which the variables are tested in a backtrack program can have a major effect on its running time. The best search order usually varies among the branches of the backtrack tree, so the number of possible search orders can be astronomical. We present an algorithm that chooses a search order dynamically by investigating all possibilities for k levels below the current level, extending beyond k levels wherever possible by setting the variables that have unique forced values. The algorithm takes time O(n k+1) to process a node. For k=2 and binary variables the analysis for selecting the next variable to introduce into the backtrack tree makes complete use of the information contained in the two-level investigations. For larger k or variables of higher degree there is no polynomial-time algorithm that makes complete use of the k-level investigations to limit searching (unless P=NP). The search rearrangement algorithm is closely related to constraint propagation. Experimental studies on conjunctive normal form predicates confirm that 1-level search rearrangement saves a great deal of time compared to 0-level (ordinary backtracking), and show that 2-level saves time over 1-level on large problems. For such problems with 256 variables 2-level is better than 1-level by a factor of two.

The Effect of Choosing the Switches for Rearrangements in Switching Networks

Known rearrangement algorithms proposed by Slepian and Paull (method 1) involve two middle switches of the three-stage Clos network. These switches are chosen arbitrarily. However, the middle switches selection rules affect the rearrangement process. In this paper four methods for choosing the switches were studied. Simulation results and analysis have shown that the allocation of the least used switches can decrease the volume of computation required for rearrangements. In the case of limited rearrangement, this method improves the blocking performance of a network.

Generalized multi‐stage connection networks

AbstractThis paper develops multi‐stage connection networks in which each input terminal can be connected to any number of output terminals. Conditions are given such that these networks are strictly nonblocking or are rearrangeable. Rearrangement algorithms and upper bounds on the required number of moves are developed and it is shown that such networks have fewer cross‐points than the product of input and output terminals for a sufficiently large number of input and output terminals.