Optimal Rotation Problems in Channel Routing

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.

A new class of cell models called Middle Terminal Model (MTM) has been proposed. In MTM, each cell contains two rows of terminals such that two terminals in a column of a cell are equipotential. Selecting an appropriate terminal row from two terminal rows available for each cell row in a standard cell design allows allocation of more over-the-cell area to the nets in congested channels. The MTM+V router is presented. It is an efficient router for MTM based standard cell designs, when vias are allowed in over-the-cell areas. The MTM+V router is based on two key algorithms, i.e., an optimal algorithm for terminal row selection and a greedy routing algorithm for over-the-cell and channel routing. >

In this paper we have developed algorithms for generating random channel instances for their use in computing channel routing solutions in VLSI physical design. Channel instances are usually of two types: simple and general, and there are usually two kinds of inherent constraints involving channel routing problem: horizontal constraint and vertical constraint. Simple channel instances do not contain any vertical constraint, whereas, general channel instances contain both horizontal as well as vertical constraints. Most of the optimization problems in two-, three-, and multi-layer channel routing are NP-hard and, in fact, very few are polynomial time computable. Hence for each of the NP-hard problems in channel routing, it is unlikely to design a polynomial time deterministic algorithm. Developing heuristic algorithm may be a probable way out that hopefully provides good solutions for most of the instances available in literature. Novelty of a heuristic algorithm is judged better if it works for a variety of large number of randomly generated instances of the problem.

The channel router, which routes a rectangular channel with two rows of terminals along its top and bottom sides, is extensively used for the automatic routing of gate arrays. It is well known that in this routing method the routing can not be performed when the vertical constraint graph contains cycles. This paper deals with the problem of eliminating cycles in the vertical constraint graph by interchanging the nets assigned to logically equivalent terminals before channel routing. A heuristic algorithm is proposed for this problem. This algorithm yields a locally optimum assignment of nets to terminals, in the sense that the number of independent cycles in the vertical constraint graph of a resultant assignment can not be reduced by interchanging any pair of the nets assigned to logically equivalent terminals. Furthermore, in order to speed up the operation of this algorithm, it is shown that the checking as to whether or not the number of independent cycles in the vertical constraint graph is reduced can be done by noting only its subgraph, when a pair of nets assigned to logically equivalent terminals are interchanged. Experimental results have indicated that this proposed algorithm is efficient.

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.

Necessary and sufficient conditions for the routability of classical channels

Channel routing for strictly multiterminal nets

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.

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>

The authors present a new three-layer over-the-cell channel routing algorithm, WILMA3 (wire length minimization algorithm 3), for high-performance circuits. This router not only minimizes the channel height by OTC routing but also minimizes the net lengths. They have also developed a two-layer router, WILMA2. Both WILMA2 and WILMA3 achieve reduction in channel height while maintaining the net length greater than its length in the two-layer channel routing. Experimental results with WILMA2 indicated that WILMA2 can produce routings that are comparable to existing two-layer over-the-cell routers. Both WILMA2 and WILMA3 achieved these results, while maintaining the net length bound. >

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.

Channel routing problem is an important, time consuming and difficult problem in VLSI layout design. In this paper, we consider the two-terminal channel routing problem in a new routing model, called knock-knee diagonal model, where the grid consists of right and left tracks displayed at +45° and –45°. An optimum algorithm is presented, which obtains d + 1 as an upper bound to the channel width, where d is the channel density.

The channel routing problem is solved using a massively parallel processor based on the artificial neural system (ANS) computational model. In this model the functional behavior of the human designer is emulated by expressing problem constraints as interconnection weights between neural cells (computational elements), using very simple computational elements for neural cells and massive parallelism to solve problems. The algorithm constraints are expressed as interconnection weights. By making the artificial neural cells work collectively on a task, a solution is obtained after each of the neural cells settles to a stable state. >

Study of algorithms and its design can be progressed in various dimensions. In this paper, we have a definite refinement of lower bound on the number of tracks required to route a channel. The attack is from a complementary viewpoint. Our algorithm succeeds to avoid all kind of approximation. The approach performs exact mapping of the problem into graphical presentation and analyzes the graph taking help of mimetic algorithm, which uses combination of sequential and GA based vertex coloring. Performance of the algorithm depends on how effectively mimetic approach can applied selecting appropriate values for the parameters to evaluate the graphical presentation of the problem. This viewpoint has immense contribution against sticking at local minima for this optimization problem. The finer result clearly exemplifies instances, which give better or at least the same lower bound in VLSI channel routing problem.Key wordsManhattan Routing modelChannel routing problemConstraint graphsMaximum Independent setMimetic algorithm

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.