Performance Driven Routing in Distributed Environment

Channel routing and crosstalk minimization are important issues while we talk about high-performance circuits for VLSI physical design automation. Interconnection among the net terminals satisfying constraints in an intelligent way is a necessity to realize a circuit in a minimum possible area, as this is a primary requirement to reduce cost as well as to increase yield. In this paper, along with area minimization, the performance of the computed circuits has also been enhanced by computing routing solutions with a specified amount of bottleneck crosstalk in two-layer channel routing. Usually, crosstalk is measured by the amount of overlapping of a pair of nets assigned to adjacent tracks. The crosstalk minimization problem in the reserved two-layer Manhattan channel routing model is NP-hard. Thus, in this paper, heuristic algorithms have been devised to optimize bottleneck crosstalk in order to augment circuit performance in two-layer channel routing. Experimental results obtained are highly encouraging.

As technology advances, interconnection wires are placed in closer proximity and circuits operate at higher frequencies. Consequently, reduction of crosstalk between interconnection wires becomes an important consideration in VLSI design. In this paper, we study the gridded channel routing problem with tbe objective of satisfying crosstalk constraints for the nets. We proposed a new approach to the problem which utilizes existing channel routing algorithms and improves upon the routing results by permuting the routing tracks. The permutation problem is proven to be NP-complete. A novel mixed ILP formulation and effective procedures for reducing the number of variables and constraints in the mixed ILP formulation are then presented. The new algorithm is tested on three large benchmark circuits as well as many randomly generated circuits. The experimental results are very promising.

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.

At the integration scale of System-On-Chips (SOCs), the conflicts between communication and computation will become prominent even on a chip. A big fraction of system time will shift from computation to communication. In synchronous systems, a large amount of communication time is spent on multiple-clock period wires. In this paper, we explore retiming to pipeline long interconnect wires in SOC designs., Behaviorally, it means that both computation and communication are rescheduled for parallelism. The retiming is applied to a netlist of macro-blocks, where the internal structures may not be changed and flip-flops may not be able to be inserted on some wire segments. This problem is different from that on a gate level netlist and is formulated as a wire retiming problem. Theoretical treatment and a polynomial time algorithm are presented in the paper. Experimental results showed the benefits and effectiveness of our approach.

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. >

Nowadays, the intense research effort is focused on exploring alternative emerging device to perform binary logical function. A promising device technology is multiferroic nanomagnet logic. The main reason for the interest in this nanomagnetic switch is its nonvolatility and comparatively low power consumption in combination with the ability to perform logic and storage in one single element. The basic element of multiferroic nanomagnet logic is a sub-100 nm size single domain magnet. Usually, the x-y direction defines the in-plane dimension, while the z axis direction depicts the thickness of nanomagnet. The in-plane magnetizations along easy axis are used to encode binary logic states 1 and 0, respectively; while along the hard axis they denote null logic. The logic operation and data transmission in magnetic logic are realized by the dipole-coupled magnetostatic interactions. In multiferroic nanomagnet logic, the interconnect wire is a very important component since it forms data transmission channel of any nanomagnetic logic circuit. There are two kinds of interconnected wires in this technology, namely antiferromagnetic coupling interconnected wire and ferromagnetic coupling interconnected wire. In this paper, the switching dynamics of a multiferroically and nanomagnetically interconnected wire employing ferromagnetic coupling is simulated by solving the Landau-Lifshitz-Gilbert equation with neglecting the thermal fluctuation effects. The wires are implemented with dipole-coupled two-phase (magnetostrictive/piezoelectric) multiferroic elements that are clocked with electrostatic potentials of 100 mV applied to the piezoelectric layer generating 20 MPa stress in the magnetostrictive layers for switching. Specifically, the ferromagnetic coupling effect model for multiferroic nanomagnet interconnected wire is established, and its magnetization dynamics is simulated by using different stress clocking. It is found that moderate strain (19.7-20.1 MPa) can ensure~180 magnetization reversal, and the logic state is successfully transferred in the ferromagnetic coupling interconnected wire. It is also found that the strong ferromagnetic coupling between multiferroic nanomagnets blocks effective magnetization reversal. This may arise from small spacing-induced out-of-plane magnetization, which does not favor the in-plane magnetization. These findings can provide some guidance for multiferroic logic circuit design.

An algorithm for finding a non-trivial lower bound for channel routing

With the increasing density of VLSI circuits, the interconnection wires are getting packed even closer. This has increased the effect of interaction between these wires on circuit performance and hence, the importance of controlling crosstalk. In this paper, we consider river routing with crosstalk constraints. Given the positions of the pins in a single-layer routing channel and the maximum tolerable crosstalk between each pair of nets, we give a polynomial time algorithm to decide whether there is a feasible river routing solution and produce one with minimum crosstalk whenever the problem is feasible.

A new channel routing model, which allows horizontal and vertical wire segments to be placed on both layers and two wires on different layers to be overlapped, is presented. Based on this model, the basic constraints as well as the rules of layer assignment and routing order in two-layer channel routing are obtained. Then the property of optimal overlapping in a zone is analyzed. For the example used, this algorithm obtains 18 tracks solution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Channel routing problem of area minimization is a well-defined problem in VLSI physical design automation. In this paper we have developed algorithms for computing reduced wire length channel routing solutions using a purely graph theoretic framework, TAH (track assignment heuristic) that was designed for computing minimum area routing solutions. Here we consider the total wire length of a routing solution as one of the most important factors of high performance computing. Reduction in wire length is important from signal delay as well as from the viewpoint of cost of wire segments required in interconnecting all the nets. The framework is designed for computing routing solutions in two-layer channels, and extended to route three-layer routing also in a modular fashion. All the algorithms developed under the framework of TAH are executed for computing no-dogleg and dogleg routing solutions for most of the well-known benchmark channels, with reduced total area and/or total wire length in two- and three-layer channel routing. Performance of our algorithms is highly encouraging.

Isolated vs. Interconnected Wind Turbine Grounding Systems: Effect on the Harmonic Grounding Impedance, Ground Potential Rise and Step Voltage

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.

This paper proposes a new power-ground (P/G) network sizing technique based on the recently proposed fast electromigration (EM) immortality check method for general multisegment interconnect wires and a new physics-based EM assessment technique for more accurate time to failure analysis. This paper first shows that the new P/G optimization problem, subject to the voltage IR drop and new EM constraints, can still be formulated as an efficient sequence of linear programing problem, where the optimization is carried out in two linear programing phases in each iteration. The new optimization will ensure that none of the wires fail if all the constraints are satisfied. However, requiring all the wires to be EM immortal can be overconstrained. To mitigate this problem, the first improvement is by means of adding reservoir branches to the mortal wires whose lifetime cannot be made immortal by wire sizing. This is a very effective approach as long as there is a sufficient reservoir area. The second improvement is to consider the aging effects of interconnect wires in the P/G networks. The idea is to allow some short-lifetime wires to fail and optimize the rest of the wires while considering the additional resistance caused by the failed wire segments. In this way, the resulting P/G networks can be optimized, such that the target lifetime of the whole P/G networks can be ensured and will become more robust and aging-aware over the expected lifetime of the chip. Numerical results on a number of IBM and self-generated power supply networks demonstrate that the new method can effectively reduce the area of the networks while ensuring immortality or enforcing target lifetime for all the wires, which is not the case for the existing current-density-constrained optimization methods.

An efficient merger of the channel routing theory and the genetic stochastic search introduces a new paradigm for VLSI channel routing. The feasibility of the paradigm is demonstrated by the first genetic router for Manhattan model channels which contain cyclic vertical constraints. The router has been implemented as a self contained genetic algorithm system. It creates an initial population without violations of constraints using the results of a new theory of locally optimal breaking of cyclic vertical constraints. The population size is problem instance dependent to provide for the preservation of the structural diversity which is built into the initial population. A new encoding scheme and novel crossover and mutation operators are introduced. Convergence rates to optimal solutions are excellent.

Polarized Fourier transform infrared (FTIR) microspectroscopy of the OH-stretching region of hydroxylapatite-chlorapatite solid solutions presents novel problems for the assignment of peaks to specific OH-Cl pairs. Crystal structure refinements of Hughes et al. (2016) identified new positions for column anions in synthetic mixed Cl-OH apatites, with three different column anion arrangements depending on composition. These structural refinements, combined with bond-valence calculations, allow for interpretation of the OH-stretching region. A peak at 3574 cm–1 is identified as that from end-member hydroxylapatite. A second major peak at 3548 cm–1 is only found in mixed chlorapatite-hydroxylapatite solid solutions, as is a third peak at 3592 cm–1. Both represent perturbations of the OH-stretching vibration as compared to hydroxylapatite, to lower and higher frequency, respectively. Both of the new peaks are the result of a Clb-OH sequence, with adjacent anions in crystallographically similar positions, both above or both below adjacent mirror planes. One configuration has the hydrogen atom pointed toward the chlorine atom. The second has the hydrogen of the OH group pointed away from the chlorine atom. Both configurations present novel problems. The shift to lower wavenumber at 3548 cm–1 is characteristic of hydrogen bonding in fluorapatite-hydroxylapatite mixtures, yet the distance between O(H) and Clb is too great to allow it. The shift of OH-stretching vibrations to lower wavenumber is produced through changes in polarization of intervening Cl-Ca2′ (or Ca2) and Ca2(′)-O3 bonds, which are affected by the presence of the large chlorine atom. Lowering the OH-stretching vibration mimics the expected effect of chlorine on a neighboring OH group in the apatite c-axis column, though without hydrogen bonding. The shift to higher wavenumbers, i.e., higher frequency at 3592 cm–1, is the opposite of that expected for hydrogen bonding between column anions in the apatite mineral group. It is ascribed to the interaction between an adjacent Clb and the oxygen end of an adjacent OH dipole. This pairing places an oxygen and a chlorine atom in close proximity. Possible means of accommodation are discussed. A ubiquitous peak at 3498 cm–1 represents hydrogen bonding between an OH and the OHa site, with an interoxygen distance of about 2.9 Å. Published modeling supports the hypothesis that the OHa site is occupied by an O rather than an OH. However, no clear counterpart to this pairing is observed in crystal structure refinements for specimens lacking OHa, although the infrared absorbance is present. The existence of oxyapatite is inferred from studies of plasma-sprayed biomaterials, but the crystal-lographic details of the substitution have remained elusive. A minor shoulder at 3517 cm–1 does not have a clear counterpart in the structural refinements. Sequences of three columnar anions (e.g., OH-Cl-OH or Cl-OH-OH) can be ruled out, but an unequivocal assignment awaits further research.