Mapping constrained optimization problems to quantum annealing with application to fault diagnosis

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.Comment: 22 pages, 4 figure

Placement-Driven Technology Mapping for LUT-Based FPGAs

In this paper, we study the problem of placement-driven technology mapping for table-lookup based FPGA architectures to optimize circuit performance. Early work on technology mapping for FPGAs such as Chortle-d[14] and Flowmap[3] aim to optimize the depth of the mapped solution without consideration of interconnect delay. Later works such as Flowmap-d[7], Bias-Clus[4] and EdgeMap consider interconnect delays during mapping, but do not take into consideration the effects of their mapping solution on the final placement. Our work focuses on the interaction between the mapping and placement stages. First, the interconnect delay information is estimated from the placement, and used during the labeling process. A placement-based mapping solution which considers both global cell congestion and local cell congestion is then developed. Finally, a legalization step and detailed placement is performed to realize the design. We have implemented our algorithm in a LUT based FPGA technology mapping package named PDM (Placement-Driven Mapping) and tested the implementation on a set of MCNC benchmarks. We use the tool VPR[1][2] for placement and routing of the mapped netlist. Experimental results show the longest path delay on a set of large MCNC benchmarks decreased by 12.3 % on the average

Layout Decomposition for Quadruple Patterning Lithography and Beyond

For next-generation technology nodes, multiple patterning lithography (MPL) has emerged as a key solution, e.g., triple patterning lithography (TPL) for 14/11nm, and quadruple patterning lithography (QPL) for sub-10nm. In this paper, we propose a generic and robust layout decomposition framework for QPL, which can be further extended to handle any general K-patterning lithography (K$>$4). Our framework is based on the semidefinite programming (SDP) formulation with novel coloring encoding. Meanwhile, we propose fast yet effective coloring assignment and achieve significant speedup. To our best knowledge, this is the first work on the general multiple patterning lithography layout decomposition.Comment: DAC'201

Throughput-driven floorplanning with wire pipelining

The size of future high-performance SoC is such that the time-of-flight of wires connecting distant pins in the layout can be much higher than the clock period. In order to keep the frequency as high as possible, the wires may be pipelined. However, the insertion of flip-flops may alter the throughput of the system due to the presence of loops in the logic netlist. In this paper, we address the problem of floorplanning a large design where long interconnects are pipelined by inserting the throughput in the cost function of a tool based on simulated annealing. The results obtained on a series of benchmarks are then validated using a simple router that breaks long interconnects by suitably placing flip-flops along the wires

Technology Mapping for Circuit Optimization Using Content-Addressable Memory

The growing complexity of Field Programmable Gate Arrays (FPGA's) is leading to architectures with high input cardinality look-up tables (LUT's). This thesis describes a methodology for area-minimizing technology mapping for combinational logic, specifically designed for such FPGA architectures. This methodology, called LURU, leverages the parallel search capabilities of Content-Addressable Memories (CAM's) to outperform traditional mapping algorithms in both execution time and quality of results. The LURU algorithm is fundamentally different from other techniques for technology mapping in that LURU uses textual string representations of circuit topology in order to efficiently store and search for circuit patterns in a CAM. A circuit is mapped to the target LUT technology using both exact and inexact string matching techniques. Common subcircuit expressions (CSE's) are also identified and used for architectural optimization---a small set of CSE's is shown to effectively cover an average of 96% of the test circuits. LURU was tested with the ISCAS'85 suite of combinational benchmark circuits and compared with the mapping algorithms FlowMap and CutMap. The area reduction shown by LURU is, on average, 20% better compared to FlowMap and CutMap. The asymptotic runtime complexity of LURU is shown to be better than that of both FlowMap and CutMap

Optimal Wheelchair Multi-LiDAR Placement for Indoor SLAM

One of the most prevalent technologies used in modern robotics is Simultaneous Localization and Mapping or, SLAM. Modern SLAM technologies usually employ a number of different probabilistic mathematics to perform processes that enable modern robots to not only map an environment but, also, concurrently localize themselves within said environment. Existing open-source SLAM technologies not only range in the different probabilistic methods they employ to achieve their task but, also, by how well the task is achieved and by their computational requirements. Additionally, the positioning of the sensors in the robot also has a substantial effect on how well these technologies work. Therefore, this dissertation is dedicated to the comparison of existing open-source ROS implemented 2D SLAM technologies and in the maximization of the performance of said SLAM technologies by researching optimal sensor placement in a Intelligent Wheelchair context, using SLAM performance as a benchmark