OPTIMIZING LARGE COMBINATIONAL NETWORKS FOR K-LUT BASED FPGA MAPPING

Optimizing by partitioning is a central problem in VLSI design automation, addressing circuit’s manufacturability. Circuit partitioning has multiple applications in VLSI design. One of the most common is that of dividing combinational circuits (usually large ones) that will not fit on a single package among a number of packages. Partitioning is of practical importance for k-LUT based FPGA circuit implementation. In this work is presented multilevel a multi-resource partitioning algorithm for partitioning large combinational circuits in order to efficiently use existing and commercially available FPGAs packagestwo-way partitioning, multi-way partitioning, recursive partitioning, flat partitioning, critical path, cutting cones, bottom-up clusters, top-down min-cut

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures

Quantum computers have recently made great strides and are on a long-term path towards useful fault-tolerant computation. A dominant overhead in fault-tolerant quantum computation is the production of high-fidelity encoded qubits, called magic states, which enable reliable error-corrected computation. We present the first detailed designs of hardware functional units that implement space-time optimized magic-state factories for surface code error-corrected machines. Interactions among distant qubits require surface code braids (physical pathways on chip) which must be routed. Magic-state factories are circuits comprised of a complex set of braids that is more difficult to route than quantum circuits considered in previous work [1]. This paper explores the impact of scheduling techniques, such as gate reordering and qubit renaming, and we propose two novel mapping techniques: braid repulsion and dipole moment braid rotation. We combine these techniques with graph partitioning and community detection algorithms, and further introduce a stitching algorithm for mapping subgraphs onto a physical machine. Our results show a factor of 5.64 reduction in space-time volume compared to the best-known previous designs for magic-state factories.Comment: 13 pages, 10 figure

Engineering applications of heuristic multilevel optimization methods

Some engineering applications of heuristic multilevel optimization methods are presented and the discussion focuses on the dependency matrix that indicates the relationship between problem functions and variables. Coordination of the subproblem optimizations is shown to be typically achieved through the use of exact or approximate sensitivity analysis. Areas for further development are identified

Structural optimization by multilevel decomposition

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem

A strategy for reducing turnaround time in design optimization using a distributed computer system

There is a need to explore methods for reducing lengthly computer turnaround or clock time associated with engineering design problems. Different strategies can be employed to reduce this turnaround time. One strategy is to run validated analysis software on a network of existing smaller computers so that portions of the computation can be done in parallel. This paper focuses on the implementation of this method using two types of problems. The first type is a traditional structural design optimization problem, which is characterized by a simple data flow and a complicated analysis. The second type of problem uses an existing computer program designed to study multilevel optimization techniques. This problem is characterized by complicated data flow and a simple analysis. The paper shows that distributed computing can be a viable means for reducing computational turnaround time for engineering design problems that lend themselves to decomposition. Parallel computing can be accomplished with a minimal cost in terms of hardware and software

The potential application of the blackboard model of problem solving to multidisciplinary design

The potential application of the blackboard model of problem solving to multidisciplinary design is discussed. Multidisciplinary design problems are complex, poorly structured, and lack a predetermined decision path from the initial starting point to the final solution. The final solution is achieved using data from different engineering disciplines. Ideally, for the final solution to be the optimum solution, there must be a significant amount of communication among the different disciplines plus intradisciplinary and interdisciplinary optimization. In reality, this is not what happens in today's sequential approach to multidisciplinary design. Therefore it is highly unlikely that the final solution is the true optimum solution from an interdisciplinary optimization standpoint. A multilevel decomposition approach is suggested as a technique to overcome the problems associated with the sequential approach, but no tool currently exists with which to fully implement this technique. A system based on the blackboard model of problem solving appears to be an ideal tool for implementing this technique because it offers an incremental problem solving approach that requires no a priori determined reasoning path. Thus it has the potential of finding a more optimum solution for the multidisciplinary design problems found in today's aerospace industries

OPTIMAL AREA AND PERFORMANCE MAPPING OF K-LUT BASED FPGAS

FPGA circuits are increasingly used in many fields: for rapid prototyping of new products (including fast ASIC implementation), for logic emulation, for producing a small number of a device, or if a device should be reconfigurable in use (reconfigurable computing). Determining if an arbitrary, given wide, function can be implemented by a programmable logic block, unfortunately, it is generally, a very difficult problem. This problem is called the Boolean matching problem. This paper introduces a new implemented algorithm able to map, both for area and performance, combinational networks using k-LUT based FPGAs.k-LUT based FPGAs, combinational circuits, performance-driven mapping.