AVF-driven Parity Optimization for MBU Protection of In-core Memory Arrays

The problem of single stuck-at, stuck-open, and stuck-on fault detection in cascode voltage switch (CVS) parity trees is considered. The results are also applied to parity and two-rail checkers. It is shown that, if the parity tree consists of only differential cascode voltage switch (DCVS) EX-OR gates, then the test set consists of at most five vectors (in some cases only four vectors are required) for detecting all detectable single stuck-at, stuck-open, and stuck-on faults, independent of the number of primary inputs and the number of inputs to any EX-OR gate in the tree. If, however, only a single-ended output is desired from the tree, then the final gate will be a single-ended cascode voltage switch (SCVS) EX-OR gate, for which the test set has only eight vectors. For a strongly self-checking (SSC) CVS parity checker, the size of a test set consisting of only codewords is nine, whereas for an SSC CVS two-rail checker the size of a test set consisting of only codewords is at most five.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effectiveness of single fault tests to detect multiple faults in parity trees

Network-on-Chip (NoC) links consume a significant fraction of the total NoC power. We present Selective Packet Interleaving (SPI), a flit transmission scheme that reduces power consumption in NoC links. SPI decreases the number of bit transitions in the links by exploiting the multiplicity of virtual channels in a NoC router. SPI multiplexes flits to the router's output link so as to minimize the number of bit transitions from the previously transmitted flit. Analysis and simulations demonstrate a reduction of up to 55% in the number of bit transitions and up to 40% savings in power consumed on the link. SPI benefits grow with the number of virtual channels. SPI works better for links with a small number of bits in parallel. While SPI compares favorably against bus inversion, combining both schemes helps to further reduce bit transitions.

Integer Linear Programming (ILP) is commonly used in high level and system level synthesis. It is an NP-Complete problem (in general cases). There exists some tools that give an optimal solution for small ILP formulations. Nevertheless, these tools may not give solutions for complex formulations. In this paper, we present a solution to overcome the problem of complexity in ILP formulations. We propose a partitioning methodology based on a constraint graph representing all the constraints included in any ILP formulation. To direct the partitioning, the constraint graph nodes are grouped to represent Data Flow Graph (DFG) nodes. This reduced constraint graph can be used to partition any ILP formulation based on DFG. We illustrate this method on ILP formulation for scheduling. Results on ILP scheduling formulations are promising.

In this paper we propose new simple integer linear programs (ILPs) formulations for minimizing capacity (in wavelength link) utilization in survivable WDM network. The study examines the performance of shared based protection schemes, such as path protection scheme and link protection scheme under single fiber failure. The numerical results obtained show a reduction in capacity utilization using random traffic compared to the reported ILP formulation. We also present the results using Poisson’s traffic to identify the frequently used links for the widely used NSF network. The proposed work not only reduces the wavelength consumption in different traffic scenarios but also efficient in terms of simulation time. In this paper we propose new simple integer linear programs (ILPs) formulations for minimizing capacity (in wavelength link) utilization in survivable WDM network. The study examines the performance of shared based protection schemes, such as path protection scheme and link protection scheme under single fiber failure. The numerical results obtained show a reduction in capacity utilization using random traffic compared to the reported ILP formulation. We also present the results using Poisson’s traffic to identify the frequently used links for the widely used NSF network. The proposed work not only reduces the wavelength consumption in different traffic scenarios but also efficient in terms of simulation time.

Recently, a biochip called MEDA (Micro Electrode Dot Array) has been studied in the field of biochemistry. During conducting experiments using a MEDA biochip, we need to move a droplet to a target position. We can split a droplet to make it smaller, and/or change its shape to go through a narrow path on a MEDA biochip. Because the velocity of a droplet is different depending on its shape and the direction of the movement, it should be complex to find an optimal routing for a droplet (i.e., to determine where to split the droplet, which path should be taken, etc.). Thus, existing methods utilize ILP (Integer Linear Programming) formulation to find an optimal routing; existing methods cannot treat large-scale problems because ILP formulation is inherently an exponential algorithm to the problem size. This paper proposes a completely new approach from the ILP formulation; our method constructs a weighted graph so that we can utilize Dijkstra's algorithm to find an optimal routing in polynomial time with respect to the chip size. Our experimental result confirms that the proposed method reduces computation time by more than 99% compared to existing ILP-based methods, and we can now find an optimal routing for a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$100 \times 100$</tex>-sized chip, which is totally impossible by existing ILP-based methods.

Exhaustive self-testing of combinational circuitry within the framework of the level-sensitive scan design (LSSD) discipline requires that every output node depend on a small number of input nodes. We present here efficient algorithms that take an arbitrary block of combinational logic and add to it the smallest number of bits of new LSSD registers necessary to: (1) partition the logic so that no output depends on more thank inputs, and (2) maintain timing within the block (so that all input-to-output paths encounter the same number of bits of register). Our partitioning algorithms conform to two different design constraints. We also show that the unconstrained partitioning problem is NP-complete.

This paper presents a technique for memory optimization for a class of computations that arises in the field of correlated electronic structure methods such as coupled cluster and configuration interaction methods in quantum chemistry. In this class of computations, loop computations perform a multi-dimensional sum of product of input arrays. There are many different ways to get the same final results that differ in the required number of arithmetic operations required. In addition, for a given number of arithmetic operations, different expressions of the loop have different memory requirements. Loop fusion is a plausible solution for reducing memory usage. By fusing loops between producer loop nest and consumer loop nest, the required storage of intermediate array is reduced by the range of the fused loop. Because resultant loops have to be legal after fusion, some loops can not be fused at the same time. In this paper, we have developed a novel integer linear programming (ILP) formulation that is shown to be highly effective on a number of test cases producing the optimal solutions using very small execution times. The main idea in the ILP formulation is the encoding of legality rules for loop fusion of a special class of loops using logical constraints over binary decision variables and a highly effective approximation of memory usage

Digital micro fluidic biochips have become one of the most promising technologies in many biomedical fields. In a digital micro fluidic biochip, a group of (adjacent) cells in the micro fluidic array can be configured to work as storage, functional operations, as well as for transporting fluid droplets dynamically. There has been proposed a very efficient Integer Linear Programming (ILP)-based method to schedule operations with considering this dynamic reconfigurability. However, the method cannot directly deal with a case having an operation with multiple successors, which is necessary in some bioassays, e.g., Sample preparation applications. Sample preparation is a crucial preprocessing step to produce droplets of the desired target concentrations from input reagents. In every optimized application graphs for sample preparation, there are many operations with more than one successors. Thus, the previous method cannot be used to get an optimal scheduling, and thus we propose a new framework to use another ILP formulation for scheduling operations in a digital micro fluidic biochips. Our formulation can successfully deal with a case where there is a node with multiple successors. Also, our method can find a binding solution at the same time unlike the above-mentioned previous one thanks to our new ILP formulation. Although our ILP formulation seems to be a bit more complex than the previous one, a preliminary experiment demonstrates that the proposed ILP formulation can successfully find the optimal scheduling for practical sample preparation applications within a reasonable time.

Summary form only given. We present a way to automatically select, within an architectural synthesis tool, the best operand and operator number systems, in order to find the best speed/area tradeoff. This implies the use of different number systems (redundant and non-redundant) for the same design: this is what we call mixed arithmetics. We present an integer linear programming (ILP) formulation to solve a scheduling problem.

In general, multicast routing and wavelength assignment (MC-RWA) can be subdivided in routing and wavelength assignment issues in wavelength-division multiplexing (WDM) mesh networks. Previous studies on WDM multicast have mainly focused on WDM multicast routing. The multicast wavelength assignment problem is studied in this paper. A unicast routing path can be established by a lightpath in an all-optical network. However, in the multicasting case, a multicast routing tree can be established by a single light-tree or several lightpaths, or a combination of several light-trees and lightpaths. We propose a wavelength assignment algorithm for finding an optimal combination of lightpaths and light-trees to construct a newly required multicast session. First of all, two cost functions are given to evaluate the establishing cost for each feasible wavelength, and then find a set of wavelengths that covers all destinations with the minimal cost using Integer Linear Programming (ILP) formulation. We focus on maximizing the total number of users served in a multicast session and the network capacity. The simulation results show that the proposed algorithm can improve system resource utilization and reduce the blocking probability compared with the First-Fit algorithm.

Coarse-grained reconfigurable array (CGRA) overlays can improve dataflow kernel throughput by an order of magnitude over Vivado HLS. This is possible with a combination of carefully floorplanned high-frequency (645-768 MHz) design and a scalable, communication-aware compiler. Our 2D torus CGRA architecture supports versatile processing element (PE) functionality and a configurable number of communication channels to match application demands. Compared to recent FPGA overlays like CGRA-ME's ADRES and HyCUBE implementations, our design operates at 1.8-3.4× faster clock frequency, while scaling to an orders-of-magnitude larger array size of 19×69 on Xilinx Alveo U280. Our communication-aware compiler targets HLS objectives such as initiation interval (II) and minimizes communication cost using an integer linear programming (ILP) formulation. Unlike SDC schedulers in FPGA HLS tools, we treat data movement as a first-class citizen by encoding the space and time resources communication network of the overlay in the ILP formulation. Given the same constraints on operational resources as Vivado HLS, we can retain our target II and achieve up to 9.2× higher frequency. Our ILP scheduler outperforms a PathFinder space-time router implementation in quality of result by up to nearly 2×.

The Fiber Installation Problem (FIP) in Wavelength Division Multiplexing (WDM) optical networks consists in routing a set of lightpaths (all-optical connections) such that the cost of the optical devices necessary to operate the network is minimized. Each of these devices is worth hundreds of thousands of dollars. In consequence, any improvement in the lightpath routing may save millions of dollars for the network operator. All the works in the literature for solving this problem are based on greedy heuristics and genetic algorithms. No information is known on how good are the solutions provided by these heuristics compared to the optimal solution. Besides, no proof that the problem is NP-Hard can be found. In this paper, we prove that FIP is NP-Hard and also present an Integer Linear Programming (ILP) formulation for the problem. In addition, we propose an implementation of the Iterated Local Search (ILS) metaheuristic to solve large instances of the problem. Computational experiments carried out on 21 realistic instances showed that the CPLEX solver running with our ILP formulation was able to solve 11 out of the 21 instances to optimality in less than two minutes. These results also showed that the ILS heuristic has an average optimality gap of 1% on the instances for which the optimal solution is known. For the other instances, the results showed that the proposed heuristic outperforms the best heuristic in the literature by 7%.

The Prize-collecting Scheduling Problem with Deadlines

We study a problem of energy-efficiently connecting a symmetric wireless communication network: given an n-vertex graph with edge weights, find a connected spanning subgraph of minimum cost, where the cost is determined by each vertex paying the heaviest edge incident to it in the subgraph. The problem is known to be NP-hard. Strengthening this hardness result, we show that even o(log n)-approximating the difference d between the optimal solution cost and a natural lower bound is NP-hard. Moreover, we show that under the exponential time hypothesis, there are no exact algorithms running in 2o(n) time or in [Formula: see text] time for any computable function f. We also show that the special case of connecting c network components with minimum additional cost generally cannot be polynomial-time reduced to instances of size cO(1) unless the polynomial-time hierarchy collapses. On the positive side, we provide an algorithm that reconnects O(log n)-connected components with minimum additional cost in polynomial time. These algorithms are motivated by application scenarios of monitoring areas or where an existing sensor network may fall apart into several connected components because of sensor faults. In experiments, the algorithm outperforms CPLEX with known integer linear programming (ILP) formulations when n is sufficiently large compared with c. Summary of Contribution: Wireless sensor networks are used to monitor air pollution, water pollution, and machine health; in forest fire and landslide detection; and in natural disaster prevention. Sensors in wireless sensor networks are often battery-powered and disposable, so one may be interested in lowering the energy consumption of the sensors in order to achieve a long lifetime of the network. We study the min-power symmetric connectivity problem, which models the task of assigning transmission powers to sensors so as to achieve a connected communication network with minimum total power consumption. The problem is NP-hard. We provide perhaps the first parameterized complexity study of optimal and approximate solutions for the problem. Our algorithms work in polynomial time in the scenario where one has to reconnect a sensor network with n sensors and O(log n)-connected components by means of a minimum transmission power increase or if one can find transmission power lower bounds that already yield a network with O(log n)-connected components. In experiments, we show that, in this scenario, our algorithms outperform previously known exact algorithms based on ILP formulations.