Algorithms for integrated circuit layout: an analytic approach
01 Nov 1980-
TL;DR: The major result presented in this dissertation is a polynomial time algorithm for a restricted case of the routing problem, which minimizes the area of a rectangle circumscribing the component and the wire paths.
Abstract: In this thesis, the problem of designing the layout of integrated circuits is examined. The layout of an integrated circuit specifies the position of the chip of functional components and wires interconnecting the components. We use a general model under which components are represented by rectangles, and wires are represented by lines. This model can be applied to circuit components defined at any level of complexity, from a transistor to a programmable logic array (PLA). We focus on the standard decomposition of the layout problem into a placement problem and a routing problem. We examine problems encountered in layout design from the point of view of complexity theory. The general layout problem under our model is shown to be NP-complete. In addition, two problems encountered in a restricted version of the routing problem --channel routing--are shown to be NP-complete. The analysis of heuristic algorithms for NP-complete problems is discussed, and the analysis of one common algorithm is presented. The major result presented in this dissertation is a polynomial time algorithm for a restricted case of the routing problem. Given one rectangular component with terminals on its boundary, and pairs of terminals to be connected, the algorithm will find a two-layer channel routing which minimizes the area of a rectangle circumscribing the component and the wire paths. Each terminal can appear in only one pair of terminals to be connected, and the rectangle used to determine the area must have its boundaries parallel to those of the component. If any of the conditions of the problem are removed, the algorithm is no longer guaranteed to find the optimal solution.
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TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
857 citations
Cites background from "Algorithms for integrated circuit l..."
...If there is only one module and only 2-terminal nets are allowed, the problem can be solved in polynomial time [15, 16 ]....
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...It is also NP-complete for nets of this form if each T i is only allowed to contain one horizontal line segment (sequence of horizontal grid segments) [15, 16 ]....
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01 Jan 1982
TL;DR: A new, “greedy”, channel-router that always succeeds, usually using no more than one track more than required by channel density, and may be forced in rare cases to make a few connections "off the end” of the channel.
Abstract: We present a new, "greedy", channel-router that is quick, simple, and highly effective. It always succeeds, usually using no more than one track more than required by channel density. (It may be forced in rare cases to make a few connections "off the end" of the channel, in order to succeed.) It assumes that all pins and wiring lie on a common grid, and that vertical wires are on one layer, horizontal on another. The greedy router wires up the channel in a left-to-right, column-by-column manner, wiring each column completely before starting the next. Within each column the router tries to maximize the utility of the wiring produced, using simple, "greedy" heuristics. It may place a net on more than one track for a few columns, and "collapse" the net to a single track later on, using a vertical jog. It may also use a jog to move a net to a track closer to its pin in some future column. The router may occasionally add a new track to the channel, to avoid "getting stuck".
291 citations
TL;DR: It is shown that an optimal set of facility locations can be drawn from a finite set of candidate points, all of which are easy to determine.
Abstract: This paper considers the optimal location of p facilities in the plane, under the assumption that all travel occurs according to the Manhattan or rectilinear or I1 metric in the presence of impenetrable barriers to travel. Facility users are distributed over a finite set of demand points, with the weight of each point proportional to its demand intensity. Each demand point is assigned to the closest facility. The objective is to locate facilities so as to minimize average Manhattan travel distance to a random demand. We show that an optimal set of facility locations can be drawn from a finite set of candidate points, all of which are easy to determine.
132 citations
27 Jun 1983
TL;DR: A new channel routing algorithm is presented, based on reduction of the problem to the case of a (2 x n) grid and on consistent utilization of a "divide and conquer" approach, which consistently outperforms several known routers in quality of wiring.
Abstract: The channel routing problem is a special care of the wire routing problem when interconnections have to be performed within a rectangular strip having no obstructions, between terminals located on opposite sides of the rectangle. We present here a new channel routing algorithm, based on reduction of the problem to the case of a (2 x n) grid and on consistent utilization of a "divide and conquer" approach. For the current implementation of the algorithm, the running time is proportional to N x n x log (m), where N is the number of nets, n is the length of the channel (number of columns) and m is the width of the channel (number of tracks). Traditional technological restrictions are assumed, i.e. net terminals are located on vertical grid lines, two wiring layers are available for interconnections - one layer is used exclusively for vertical segments, another for horizontal and vias are introduced for each layer change. This algorithm consistently outperforms several known routers in quality of wiring. We tested the algorithm on several benchmark problems. One of them - Deutsch's "difficult example" - was routed with only 19 horizontal wiring tracks (the absolute minimum for this case), whereas all other known routers required 20 or more tracks.
116 citations