Routing for analog chip designs at NXP Semiconductors

During the study week 2011 we worked on the question of how to automate certain aspects of the design of analog chips. Here we focused on the task of connecting different blocks with electrical wiring, which is particularly tedious to do by hand. For digital chips there is a wealth of research available for this, as in this situation the amount of blocks makes it hopeless to do the design by hand. Hence, we set our task to finding solutions that are based on the previous research, as well as being tailored to the specific setting given by NXP. This resulted in an heuristic approach, which we presented at the end of the week in the form of a protoype tool. In this report we give a detailed account of the ideas we used, and describe possibilities to extend the approach

Using ant colony optimization for routing in microprocesors

Power consumption is an important constraint on VLSI systems. With the advancement in technology, it is now possible to pack a large range of functionalities into VLSI devices. Hence it is important to find out ways to utilize these functionalities with optimized power consumption. This work focuses on curbing power consumption at the design stage. This work emphasizes minimizing active power consumption by minimizing the load capacitance of the chip. Capacitance of wires and vias can be minimized using Ant Colony Optimization (ACO) algorithms. ACO provides a multi agent framework for combinatorial optimization problems and hence is used to handle multiple constraints of minimizing wire-length and vias to achieve the goal of minimizing capacitance and hence power consumption. The ACO developed here is able to achieve an 8% reduction of wire-length and 7% reduction in vias thereby providing a 7% reduction in total capacitance, compared to other state of the art routers

Shortest Paths and Steiner Trees in VLSI Routing

Routing is one of the major steps in very-large-scale integration (VLSI) design. Its task is to find disjoint wire connections between sets of points on a chip, subject to numerous constraints. This problem is solved in a two-stage approach, which consists of so-called global and detailed routing steps. For each set of metal components to be connected, global routing reduces the search space by computing corridors in which detailed routing sequentially determines the desired connections as shortest paths. In this thesis, we present new theoretical results on Steiner trees and shortest paths, the two main mathematical concepts in routing. In the practical part, we give computational results of BonnRoute, a VLSI routing tool developed at the Research Institute for Discrete Mathematics at the University of Bonn. Interconnect signal delays are becoming increasingly important in modern chip designs. Therefore, the length of paths or direct delay measures should be taken into account when constructing rectilinear Steiner trees. We consider the problem of finding a rectilinear Steiner minimum tree (RSMT) that --- as a secondary objective --- minimizes a signal delay related objective. Given a source we derive some structural properties of RSMTs for which the weighted sum of path lengths from the source to the other terminals is minimized. Also, we present an exact algorithm for constructing RSMTs with weighted sum of path lengths as secondary objective, and a heuristic for various secondary objectives. Computational results for industrial designs are presented. We further consider the problem of finding a shortest rectilinear Steiner tree in the plane in the presence of rectilinear obstacles. The Steiner tree is allowed to run over obstacles; however, if it intersects an obstacle, then no connected component of the induced subtree must be longer than a given fixed length. This kind of length restriction is motivated by its application in VLSI routing where a large Steiner tree requires the insertion of repeaters which must not be placed on top of obstacles. We show that there are optimal length-restricted Steiner trees with a special structure. In particular, we prove that a certain graph (called augmented Hanan grid) always contains an optimal solution. Based on this structural result, we give an approximation scheme for the special case that all obstacles are of rectangular shape or are represented by at most a constant number of edges. Turning to the shortest paths problem, we present a new generic framework for Dijkstra's algorithm for finding shortest paths in digraphs with non-negative integral edge lengths. Instead of labeling individual vertices, we label subgraphs which partition the given graph. Much better running times can be achieved if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy. As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, the algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goal-oriented techniques leads to considerably reduced running time. We illustrate this with the routing program BonnRoute on leading-edge industrial chips. Finally, we present computational results of BonnRoute obtained on real-world VLSI chips. BonnRoute fulfills all requirements of modern VLSI routing and has been used by IBM and its customers over many years to produce more than one thousand different chips. To demonstrate the strength of BonnRoute as a state-of-the-art industrial routing tool, we show that it performs excellently on all traditional quality measures such as wire length and number of vias, but also on further criteria of equal importance in the every-day work of the designer

A parallel genetic algorithm for the Steiner Problem in Networks

This paper presents a parallel genetic algorithm to the Steiner Problem in Networks. Several previous papers have proposed the adoption of GAs and others metaheuristics to solve the SPN demonstrating the validity of their approaches. This work differs from them for two main reasons: the dimension and the characteristics of the networks adopted in the experiments and the aim from which it has been originated. The reason that aimed this work was namely to build a comparison term for validating deterministic and computationally inexpensive algorithms which can be used in practical engineering applications, such as the multicast transmission in the Internet. On the other hand, the large dimensions of our sample networks require the adoption of a parallel implementation of the Steiner GA, which is able to deal with such large problem instances

An Improved Augmented Line Segment based Algorithm for the Generation of Rectilinear Steiner Minimum Tree

An improved Augmented Line Segment Based (ALSB) algorithm for the construction of Rectilinear Steiner Minimum Tree using augmented line segments is proposed. The proposed algorithm works by incrementally increasing the length of line segments drawn from all the points in four directions. The edges are incrementally added to the tree when two line segments intersect. The reduction in cost is obtained by postponing the addition of the edge into the tree when both the edges (upper and lower L-shaped layouts) are of same length or there is no overlap. The improvement is focused on reduction of the cost of the tree and the number of times the line segments are augmented. Instead of increasing the length of line segments by 1, the line segments length are doubled each time until they cross the intersection point between them. The proposed algorithm reduces the wire length and produces good reduction in the number of times the line segments are incremented. Rectilinear Steiner Minimum Tree has the main application in the global routing phase of VLSI design. The proposed improved ALSB algorithm efficiently constructs RSMT for the set of circuits in IBM benchmark

Timing-Constrained Global Routing with RC-Aware Steiner Trees and Routing Based Optimization

In this thesis we consider the global routing problem, which arises as one of the major subproblems in the physical design step in VLSI design. In global routing, we are given a three-dimensional grid graph G with edge capacities representing available routing space, and we have to connect a set of nets in G without overusing any edge capacities. Here, each net consists of a set of pins corresponding to vertices of G, where one pin is the sender of signals, while all other pins are receivers. Traditionally, next to obeying all edge capacity constraints, the objective has been to minimize wire length and possibly via (edges in z-direction) count, and timing constraints on the chip were only modeled indirectly. We present a new approach, where timing constraints are modeled directly during global routing: In joint work with Stephan Held, Dirk Mueller, Daniel Rotter, Vera Traub and Jens Vygen, we extend the modeling of global routing as a Min-Max Resource Sharing Problem to also incorporate timing constraints. For measuring signal delays we use the well-established Elmore delay model. One of the key subproblems here is the computation of Steiner trees minimizing a weighted sum of routing space usages and signal delays. For k pins, this problem is NP-hard to approximate within o(log k), and even the special case k = 2 is NP-hard, as was shown by Haehnle and Rotter. We present a fast approximation algorithm with strong approximation bounds for the case k = 2. For k > 2 we use a multi-stage approach based on modifying the topology of a short Steiner tree and using our algorithm for the two-pin case for computing new connections. Moreover, we present a layer assignment algorithm that assigns z-coordinates to the edges of a given two-dimensional tree. We also discuss the topic of routing based optimization. Here, the starting point is a complete routing, and timing optimization tools make changes that require incremental adaptations of the underlying routing. We investigate several aspects of this problem and derive a new routing flow that includes our timing-aware global router and routing based optimization steps. We evaluate our results from this thesis in practice on industrial 14nm microprocessor designs from IBM. Our theoretical results are validated in practice by a strong performance of our timing-aware global routing framework and our new routing flow, yielding significant improvements over the traditional global routing method and the previously used routing flow. Therefore, we conclude that our approaches and results from this thesis are not only theoretically sound but also give compelling results in practice

Netlist Decomposition and Candidate Generation for Analog IC Routing

Netlist decomposition and candidate generation is a non-conventional approach in the routing stage of the place and route (PnR) flow. While there has been significant research and advancement in the digital domain for automation with respect to this as well as other techniques, very little work has been done in the analog domain due to its complex constraints and specific requirements. With this proposed method, the most common requirements of Analog circuits are taken into consideration to provide candidate routes for netlists of analog Integrated Chips (IC). Netlist decomposition is an important stage of breaking down multi-pin nets into two-pin nets by adding additional nodes for each net. The proposed method takes into account blockages and constraints such as symmetry and bends to develop a new algorithm using Steiner trees and Hanan grids to generate optimal Steiner points. This method also breaks down multi-pin nets to 3-pin nets which reduces the wirelength and computations significantly. The decomposed net segments are run through Dijkstra algorithm to generate multiple candidates and an Integer Linear programming (ILP) solver is used to pick the best candidates that follow all the constraints and design rules. The experimental results show that overall wirelength is reduced by 5.16% while using 3-pin net decomposition when compared to 2-pin net decomposition. There is also a reduction in the number of metal layers used and the number of Steiner points generated. The method shows lesser computations when compared to other decomposition techniques as it avoids multiple reroutes to obtain Design Rule Check (DRC) clean routes

Netlist Decomposition and Candidate Generation for Analog IC Routing

Netlist decomposition and candidate generation is a non-conventional approach in the routing stage of the place and route (PnR) flow. While there has been significant research and advancement in the digital domain for automation with respect to this as well as other techniques, very little work has been done in the analog domain due to its complex constraints and specific requirements. With this proposed method, the most common requirements of Analog circuits are taken into consideration to provide candidate routes for netlists of analog Integrated Chips (IC). Netlist decomposition is an important stage of breaking down multi-pin nets into two-pin nets by adding additional nodes for each net. The proposed method takes into account blockages and constraints such as symmetry and bends to develop a new algorithm using Steiner trees and Hanan grids to generate optimal Steiner points. This method also breaks down multi-pin nets to 3-pin nets which reduces the wirelength and computations significantly. The decomposed net segments are run through Dijkstra algorithm to generate multiple candidates and an Integer Linear programming (ILP) solver is used to pick the best candidates that follow all the constraints and design rules. The experimental results show that overall wirelength is reduced by 5.16% while using 3-pin net decomposition when compared to 2-pin net decomposition. There is also a reduction in the number of metal layers used and the number of Steiner points generated. The method shows lesser computations when compared to other decomposition techniques as it avoids multiple reroutes to obtain Design Rule Check (DRC) clean routes

A complete design path for the layout of flexible macros

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