Algorithms for Generating Random Channel Instances for Channel Routing Problem

Demonstrates that the vertical constraint graph (VCG) is not a complete representation of the vertical constraints of a channel, and proposes an edge-weight augmented VCG that is proved to be complete. Examples demonstrate the feasibility of a deterministic approach to the locally optimal resolution of cyclic vertical constraints when the information provided by the new model is used. >

Locally optimal breaking strategy was already developed for disjoint directed circuits in the vertical constraint graph. The paper reports extensions to two classes of nondisjoint circuits: with a common vertex, and with a common path. The significance of this is that the demonstration of general applicability of the locally optimal breaking concept opens a new approach to improving the channel router heuristics for automatic and interactive routers, using parallel architectures.

An important part of the integrated circuit design process is the channel routing stage, which determines how to interconnect components that are arranged in sets of rows. The channel routing problem has been shown to be NP-complete, thus this problem is often solved using genetic algorithms. The traditional objective for most channel routers is to minimize total area required to complete routing. However, another important objective is to minimize signal propagation delays in the circuit. This paper describes the development of a genetic channel routing algorithm that uses a Pareto-optimal approach to accommodate both objectives. When compared to the traditional channel routing approach, the new channel router produced layouts with decreased signal delay, while still minimizing routing area.

As the very large scale integration (VLSI) technology approaches its fundamental scaling limit at about 0.2 /spl mu/m, it is reasonable to consider three-dimensional (3-D) integration to enhance packing density and speed performance. With additional functional units packed into one chip in a 3-D space, computer-aided design (CAD) tools are demanded to ease the complicated design work. This paper presents a 100% completion achievable routing methodology. The routing methodology is based on the two-dimensional (2D) channel routing methodology; thus, it is called a 3-D channel routing methodology. With the routing methodology, a 3-D routing problem is decomposed into two 2D routing subproblems: intra-layer routing that interconnects terminals on the same layer, which can be done by using a 2-D channel router, and inter-layer routing that interconnects terminals on different layers. The inter-layer routing problem is transformed into a 2-D channel routing problem and the transformation is made in some 3-D channels. Detailed discussions are given for the 3-D to 2-D transformation. Optimization of the transformation is shown to be NP-complete. Thus, simulated annealing is used to optimize the transformation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

As fabrication technology advances, devices and interconnection wires are placed in closer proximity and circuits operate at higher frequencies. This results in crosstalk between wire segments. Work on routing channels with reduced crosstalk is a very important area of current research [3],[10]. We know that the crosstalk minimization problem in the reserved two-layer Manhattan routing model is NP-complete, even for the channels without any vertical constraints. Since minimizing crosstalk is NP-complete, several polynomial time heuristic algorithms for reducing crosstalk have been developed [8],[9], [15]. All the ideas that are introduced as heuristics are basically sequential in nature. In this paper we have developed two efficient heuristics to compute reduced crosstalk routing solutions in a distributed computing environment. Our proposed heuristics are much better in computational complexity than the existing sequential versions of the algorithms developed in [9], [15].KeywordsBlank SpaceWire SegmentDistribute Computing EnvironmentParallel Random Access MachineTotal SpanThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Recently, multi-trace impedance inversion has attracted great interest in seismic exploration because it improves the horizontal continuity and fidelity of the inversion results by exploiting the lateral structure information of the strata. However, computational inefficiency affects its practical application. Furthermore, in terms of vertical constraints on the model parameters, it only considers smooth features while ignoring sharp discontinuity features. This leads to yielding an over-smooth solution that does not accurately reflect the distribution of underground rock. To deal with the above situations, we first develop a low-dimensional multi-trace impedance inversion (LMII) framework. Inspired by compressed sensing, this framework utilizes low-dimensional measurements in sparse space containing the maximum information of the signal to construct the objective function for multi-trace inversion, which can significantly reduce the size of the inversion problem and improve the inverse efficiency. Then, we introduce the elastic half (EH) norm as a vertical constraint on the model parameters in the LMII framework and formulate a novel constrained LMII model for impedance inversion. Because the introduced EH norm takes into account both the smoothness and blockiness of rock impedance, the constrained LMII model can effectively raise the inversion accuracy of complex strata. Finally, an efficient alternating multiplier iteration algorithm is derived based on the variable splitting technique to optimize the constrained LMII model. The performance of the developed approaches is tested using synthetic and practical data, and the results prove their feasibility and superiority.

Necessary and sufficient conditions for the routability of classical channels

This paper presents a "preprocessor" which separates a channel routing problem into two subproblems. One is a specialized channel routing problem where no two nodes of two different nets are of the same y-grid position. The other is a problem of connecting pairs of nodes where each pair of nodes has a path reserved for it. The use of a "preprocessor" in channel routing [5] is justified by the comparison of routing results.

Channel routing for strictly multiterminal nets

Wireless mesh networks are being deployed all around the world both to provide ubiquitous connection to the Internet and to carry data generated by several services (video surveillance, smart grids, earthquake early warning systems, etc.). In those cases where fixed power connections are not available, mesh nodes operate by harvesting ambient energy (e.g., solar or wind power) and hence they can count on a limited and time-varying amount of power to accomplish their functions. Since we consider mesh nodes equipped with multiple radios, power savings and network performance can be maximized by properly routing flows, assigning channels to radios and identifying nodes/radios that can be turned off . Thus, the problem we address is a joint channel assignment and routing problem with additional constraints on the node power consumption, which is NP-complete. In this paper, we propose a heuristic, named minimum power channel assignment and routing algorithm (MP-CARA), which is guaranteed to return a local optimum for this problem. Based on a theoretical analysis that we present in the paper, which gives an upper bound on the outage probability as a function of the constraint on power consumption, we can guarantee that the probability that a node runs out of power with MP-CARA falls below a desired threshold. The performance of MP-CARA is assessed by means of an extensive simulation study aiming to compare the solutions returned by MP-CARA to those found by other heuristics proposed in the literature.

For multi-radio multi-channel wireless mesh networks (WMNs), the joint channel assignment and routing problem has been shown to be NP-complete. In this paper, we first use a rate-variable model to increase the network through output, which use the physical interference model that can evaluate the capacity more precisely. Then we present a mathematical programming model which allows us to formulate the task of deriving joint channel assignment and routing as an integer linear programming problem. Simulation results show that the proposed approach effectively increases the network through output.

In Cognitive Radio Mesh Networks (CogMesh), Secondary Mesh Routers (SMRs) can opportunistically utilize the licensed spectrums for the traffic of the Secondary Mesh Users (SMUs). How to guarantee Quality of Service (QoS) for real-time services over CogMesh is still an opening issue. In this paper, we present a discrete-time vacation queueing system to abstract the Primary User (PU) interruption to SMR data transmission. Moreover, we formulate the optimization problem of joint channel selection and routing, to achieve minimum end-to-end delay for SMR while guaranteeing the channel unavailability. A heuristic method is proposed to solve this problem and results show our proposed method performs the closest to the scheme using optimization tool, and outperforms the minimal unavailability scheme and minimal delay scheme in terms of end-to-end delay and solution rate.Keywordscognitive radio mesh networksreal-time servicesvacation queueingchannel selection

A parallel algorithm is proposed for solving the problem of channel and switchbox routing in the design of VLSI chips. The algorithm is suitable for implementation on a shared-memory multiprocessor environment. Our approach does not impose restrictions on the channel type (such as fix or variable channel widths) and the number of available layers. The algorithm contains three major phases: 1) dividing the channel into several regions by selecting some columns, 2) assigning tracks to nets of the selected columns, and 3) assigning tracks to nets of the columns in each region.

In the channel routing problem, terminals between cells are interconnected completely while reducing channel routing area. The crossing number, the number of crossings between two wires in the channel, is related to the channel routing area. In this paper, we present a parallel algorithm finding a maximum crossing number, density, in the channel by using a LARPBS model (Linear Array with a Reconfigurable Pipelined Bus System), which is based on the advanced fiber optic technology. The maximum crossing number algorithm on the LARPBS model runs in O(n) time using O(n) number of processors, where n is the number of nets in a channel.

We present an algorithm to find a set of all optimal solutions for a channel placement problem. A channel consists of two rows of horizontal line segments (representing components). Each line segment contains some terminals with fixed positions. Sets of terminals, called nets, are to be connected. The relative ordering of line segments in each row is fixed. The line segments can be shifted left or right, which will affect the width needed for routing and the length of the channel. We want to find the tradeoff between channel length and routing width. Since the channel routing problem is NP-complete, we use a lower bound on routing width, called density. The density of a placement is the maximum number of nets crossing each vertical cut. We can increase the total length to minimize the channel density, or minimize the total length by increasing the channel density. The pair (density, total length) is called the shape of a placement. A shape is minimal if a decrease in density would cause an increase in total length, and vice versa. Our algorithm computes all the minimal shapes in O (N 4 ) time, where N is the number of nets. This is the first known algorithm for this problem whose running time is polynomial in the number of nets and independent of the length of the channel.