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This paper presents a comprehensive study of the computation of square roots over finite extension fields. We propose two novel algorithms for computing square roots over even field extensions of the form \BBF{q^2}, with q = p^n, p an odd prime and n \geq 1. Both algorithms have an associate computational cost roughly equivalent to one exponentiation in \BBF{q^2}. The first algorithm is devoted to the case when q \equiv 1\, mod\, 4, whereas the second one handles the case when q \equiv 3\, mod\,4. Numerical comparisons show that the two algorithms presented in this paper are competitive and in some cases more efficient than the square root methods previously known. [ABSTRACT FROM AUTHOR]

Grid computing is a newly emerging technology aimed at large-scale resource sharing and global-area collaboration. It is the next step in the evolution of parallel and distributed computing. Due to the largeness and complexity of the grid system, its performance and reliability are difficult to model, analyze, and evaluate. This paper presents a model that relaxes some assumptions made in prior research on distributed systems that were inappropriate for grid computing. The paper proposes a virtual tree-structured model of the grid service. This model simplifies the physical structure of a grid service, allows service performance (execution time) to be efficiently evaluated, and takes into account data dependence and failure correlation. Based on the model, an algorithm for evaluating the grid service time distribution and the service reliability indices is suggested. The algorithm is based on Graph theory and probability theory. Illustrative examples and a real case study of the BioGrid are presented. [ABSTRACT FROM AUTHOR]

As the demand for high-quality Internet increases, emerging network applications are spurring the need for faster, feature-rich, and cost-effective routers. Multifield packet classification in routers has been a computation-intensive data path function for software implementation. Therefore, solutions for packet classification based on hardware design, such as Ternary Content Addressable Memory (TCAM), are necessary to sustain gigabit line processing rate. Traditionally, TCAMs have been designed for storing prefixes. However, multifield packet classification usually involves two fields of arbitrary ranges that are TCP/IP layer 4 source and destination ports. Storing ranges in TCAMs relies on decomposing each individual range into multiple prefixes, which leads to range-to-prefix blowout. To reduce the total number of prefixes needed to represent all ranges, this paper proposes a 2-level TCAM architecture and two range-to-prefix conversion schemes. In the first proposed scheme, designed for disjoint ranges, the maximum number of entries needed in TCAM is 2m - 1 for m disjoint ranges. In the second proposed scheme, designed for contiguous ranges, only m TCAM entries are needed. In a general case of n arbitrary ranges, all ranges can first be converted into disjoint ranges or contiguous ranges and then the proposed algorithms can be applied. As a result, only 4n - 3 TCAM entries are needed for the disjoint ranges and only 2n + 1 TCAM entries are needed for contiguous ranges. This paper also proposes insertion and deletion algorithms to accommodate incremental changes to the range sets. The experiments made show that the proposed range-to-prefix conversion schemes perform better than the existing schemes in terms of the number of required TCAM entries and execution time for range update operations. [ABSTRACT FROM AUTHOR]

Wearable computing has recently gained much popularity as an ambitious vision for future personalized mobile systems. Its aim is intelligent, environment aware systems unobtrusively embedded into the mobile environments of their users. With the combination of complex processing requirements, the necessity of placing sensors and input/output modules at different locations on the user's body, and stringent limits on size, weight, and battery capacity, the design of such systems is an inherently challenging problem. This paper demonstrates how systematic design and quantitative analysis can be applied to wearable architectures. We first present a model that allows various factors influencing the design of a wearable system to be incorporated into formal cost metrics. In particular, we show how to consistently incorporate specific wearable factors such as device placement requirements, ergonomics, and dynamic workload profiles into the model. We then discuss how efficient estimation algorithms can be extended and applied to the evaluation of different architectures with respect to our cost metrics. Finally, we discuss quantitative results from a proof-of-concept case study showing the trade offs between different architectures for a given wearable scenario. Summarized, this paper demonstrates how the description and the design of wearable systems can be put on a systematic, formal basis allowing us to treat them similar as conventional embedded systems. [ABSTRACT FROM AUTHOR]

In modern SoCs embedded memories should be protected by ECC against field failures to achieve acceptable reliability. They should also be repaired after fabrication to achieve acceptable fabrication yield. In technologies affected by high defect densities, conventional repair induces very high costs. To reduce it, we can use ECC-based repair, consisting in using the ECC for fixing words comprising a single faulty cell and self-repair to fix all other faulty words. However, as we show in this paper, for high defect densities the diagnosis circuitry required for ECC-based repair may induce very large hardware cost. To fix this issue, we introduce a new family of memory test algorithms that exhibit a property we termed as “single-read double-fault detection”. This approach gains interest in ultimate CMOS and post-CMOS technologies, where the defect densities are expected to increase significantly, and/or in very-low power design, as very-low voltage sharply increases defect densities. [ABSTRACT FROM PUBLISHER]

In this paper we study the problem of characterizing and exploiting the complete flexibility of a special logic architecture, called P-circuits, which realize a Boolean function by projecting it onto overlapping subsets given by a generalized Shannon decomposition. P-circuits are used to restructure logic by pushing some signals towards the outputs. The algorithms proposed so far for exploiting the structural flexibility of P-circuits do not guarantee to find the best implementation, because they cast the problem as the minimization of an incompletely specified function. Instead, here we show that to explore all solutions we must set up the problem as the minimization of a Boolean relation, because there are don’t care conditions that cannot be expressed by single cubes. Finally we report the results obtained using a minimizer of Boolean relations, which improve in a major way with respect to the previous literature. [ABSTRACT FROM PUBLISHER]

Task period selection is often used to adjust the workload to the available computational resources. In this paper, we propose a model where each selected period is not restricted to be a natural number, but can be any rational number within a range. Under this generalization, we contribute a period selection algorithm that yields a much smaller hyperperiod than that of previous works: with respect to the largest period, the hyperperiod with integer constraints is exponentially bounded; with rational periods the worst case is only quadratic. By means of an integer approximation at each task activation, we show how our rational period approach can work under system clock granularity; it is thus compatible with scheduling analysis practice and implementation. Our finding has practical applications in several fields of real-time scheduling: lowering complexity in table driven schedulers, reducing search space in model checking analysis, generating synthetic workload for statistical analysis of real-time scheduling algorithms, etc. [ABSTRACT FROM AUTHOR]

In testing from a Finite State Machine (FSM), the generation of test suites which guarantee full fault detection, known as complete test suites, has been a long-standing research topic. In this paper, we present conditions that are sufficient for a test suite to be complete. We demonstrate that the existing conditions are special cases of the proposed ones. An algorithm that checks whether a given test suite is complete is given. The experimental results show that the algorithm can be used for relatively large FSMs and test suites. [ABSTRACT FROM AUTHOR]

Hard real-time systems always choose not to use garbage collection in order to avoid its unpredictable executions. Much effort has been expended trying to build predictable garbage collectors which can provide both temporal and spatial guarantees. Unfortunately, most existing work leads to systems that cannot easily achieve a balance between temporal and spatial performances. Moreover, the scheduling of garbage collectors has not been integrated into modern real-time scheduling frameworks, which makes the benefits provided by the advancement of scheduling techniques very difficult to obtain. This paper argues that the existing design criteria for real-time garbage collectors do not reflect the unique requirements of flexible hard real-time systems. As a part of our design criteria, a new performance indicator is proposed to describe the capability of a real-time garbage collector to achieve a better balance between temporal and spatial performances. A hybrid garbage collection algorithm is designed accordingly which also uses dual priority scheduling algorithm to reclaim spare capacity while guaranteeing deadlines. [ABSTRACT FROM AUTHOR]

This paper presents an efficient adaptive online routing algorithm for the computation of bandwidth-guaranteed paths in Multiprotocol Label Switching (MPLS)-based networks by using a learning scheme that computes an optimal ordering of routes. The contribution of this work is twofold. The first is that we propose a new class of solutions other than those available in the literature, incorporating the family of stochastic Random Races (RR) algorithms. The most popular previously proposed MPLS-based Traffic Engineering (TE) solutions attempt to find a superior path to route an incoming setup request. Our algorithm, on the other hand, tries to learn an optimal ordering of the paths through which requests can be routed according to the rank of the paths in the order learned by the algorithm. The second contribution of our work is that we have proposed a routing algorithm that has a performance superior to the important algorithms in the literature. Our conclusions are based on three important performance criteria: 1) the rejection ratio, 2) the percentage of accepted bandwidth, and 3) the average route computation time per request. Although some of the previously proposed algorithms were designed to achieve low rejection and high throughput of route requests, they are unreasonably slow. Our algorithm, on the other hand, in general attempts to reject the least number of requests, achieves the highest throughput, and computes routes in the fastest possible time when compared to the algorithms that we used as benchmarks for comparison. [ABSTRACT FROM AUTHOR]

The physical security of application-specific embedded processors such as those found in smart-cards has become increasingly important since they are used more and more as conduits for sensitive financial and identity information. The advent of side-channel attacks has meant that a combination of algorithm, software, and hardware defense is required. In this paper, we reexamine the issue of nondeterministic processors, simplifying previous designs using a multithreaded architecture. From this simplification, we are able to construct a formally reasoned assessment of the security level offered by such a device. [ABSTRACT FROM AUTHOR]

In this paper, we propose load distribution strategies for divisible loads for networked computing environments where computation and communication resource characteristics are unknown and/or vary with time. The principle on which our strategies are formulated is based on using probing loads to estimate the network characteristics and using them to determine the best possible load distribution. This work extends the adaptive strategies proposed in an earlier work to multilevel general networks. These networks, while being more challenging, also offer several opportunities that can be exploited to make the probing phase more efficient. We propose two strategies, one static, which caters to the presence of unknown parameters, and the other dynamic, which caters to both unknown as well as time-varying network parameters. The proposed strategies are robust, resilient, and easily adaptable to network fluctuations. The algorithms are also shown to have a tracking ability, a property that is important in dynamic environments. Examples are presented to illustrate the salient features of these strategies. [ABSTRACT FROM AUTHOR]

In many emerging time-critical applications, the exact time of event occurrences may not be known. In such cases, events can be represented as a probabilistic occurrence within a time interval. Thus, monitoring of timing constraints, generally used in time-critical systems, needs to incorporate the uncertainty of event occurrences. In this paper, we propose mechanisms to monitor the satisfaction/violation of timing constraints that can be assessed probabilistically. We assume a uniform distribution of event occurrence within a time interval. Our proposed algorithm determines whether the probability that a timing constraint has been satisfied exceeds a specified threshold value. A confidence threshold is a minimum satisfaction probability of the timing constraint. A timing constraint is violated if the confidence threshold is not reached. We design an efficient monitoring algorithm for detecting timing violations of a set of timing constraints by finding the earliest expiration time (EET) for each timing constraint. Since it is critical to derive implicit constraints for early detection of violation of timing constraints, we present the derivation of the implicit constraints under uncertainty using an all-pairs shortest path algorithm. Further, we propose pruning techniques to discard unnecessary implicit constraints. We present the properties and proofs of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel sensor deployment algorithm, called the adaptive triangular deployment (ATRI) algorithm, for large-scale unattended mobile sensor networks. The ATRI algorithm aims at maximizing coverage area and minimizing coverage gaps and overlaps by adjusting the deployment layout of nodes close to equilateral triangulation, which is proven to be the optimal layout to provide the maximum no-gap coverage. The algorithm only needs the location information of nearby nodes, thereby avoiding communication cost for exchanging global information. By dividing the transmission range into six sectors, each node adjusts the relative distance to its one-hop neighbors in each sector separately. The distance threshold strategy and the movement state diagram strategy are adopted to avoid the oscillation of nodes. The simulation results show that the ATRI algorithm achieves a much larger coverage area and smaller average moving distance of nodes than existing algorithms. We also show that the ATRI algorithm is applicable to practical environments and tasks such as working in both bounded and unbounded areas and avoiding irregularly shaped obstacles. In addition, the density of nodes can be adjusted adaptively to different requirements of tasks. [ABSTRACT FROM AUTHOR]

System-level diagnosis aims at the identification of faulty units in a system by the analysis of the system syndrome, that is, the outcomes of a set of interunit tests. For any given syndrome, it is possible to produce a correct (although possibly incomplete) diagnosis of the system if the number of faults is below a syndrome-dependent bound and the degree of diagnosis completeness, that is, the number of correctly diagnosed units, is also dependent on the actual syndrome σ. The worst-case diagnosis completeness is a syndrome-independent bound that represents the minimum number of units that the diagnosis algorithm correctly diagnoses for any syndrome. This paper provides a lower bound to the worst-case diagnosis completeness for regular graphs for which vertex- isoperimetric inequalities are known and it shows how this bound can be applied to toroidal grids. These results prove a previous hypothesis about the influence of two topological parameters of the diagnostic graph, that is, the bisection width and the diameter, on the degree of diagnosis completeness. [ABSTRACT FROM AUTHOR]

A fundamental challenge in improving file system performance is to design effective block replacement algorithms to minimize buffer cache misses. Despite the well-known interactions between prefetching and caching, almost all buffer cache replacement algorithms have been proposed and studied comparatively, without taking into account file system prefetching, which exists in all modern operating systems. This paper shows that such kernel prefetching can have a significant impact on the relative performance in terms of the number of actual disk I/Os of many well-known replacement algorithms; it can not only narrow the performance gap but also change the relative performance benefits of different algorithms. Moreover, since prefetching can increase the number of blocks clustered for each disk I/O and, hence, the time to complete the I/O, the reduction in the number of disk I/Os may not translate into proportional reduction in the total I/O time. These results demonstrate the importance of buffer caching research taking file system prefetching into consideration and comparing the actual disk I/Os and the execution time under different replacement algorithms. [ABSTRACT FROM AUTHOR]

Alternating group graphs AGn, studied by Jwo and others, Constitute a class of Cayley graphs that possess certain desirable properties compared with other regular networks considered by researchers in parallel and distributed computing. A different form, ANn, of such graphs, proposed by Youhou and dubbed alternating group networks, has been shown to possess advantages over AGn. For example, ANn has a node degree that is smaller by a factor of about 2 while maintaining a diameter comparable to that of AGn, is maximally fault-tolerant, and shares some of the positive structural attributes of the well-known star graph. In this paper, we characterize the distance between any two nodes in ANn and present an optimal (shortest-path) routing algorithm for this class of networks. [ABSTRACT FROM AUTHOR]

This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a POPS(d, g) network either with O(d/g log g) deterministic slots, or, with high probability, with 5c[d/g] + o(d/g) + O(log log g) randomized slots, where constant c = exp(1 + e-1) ≈ 3.927. When d = ϴ(g), which we claim to be the ‘interesting’ case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2, 2) and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance. [ABSTRACT FROM AUTHOR]

A Taylor Expansion Diagram (TED) is a compact, word-level, canonical representation for data flow computations that can be expressed as multivariate polynomials. TEDs are based on a decomposition scheme using Taylor series expansion that allows one to model word-level signals as algebraic symbols. This power of abstraction, combined with the canonicity and compactness of TED, makes it applicable to equivalence verification of dataflow designs. The paper describes the theory of TEDs and proves their canonicity. It shows how to construct a TED from an HDL design specification and discusses the application of TEDs in proving the equivalence of such designs. Experiments were performed with a variety of designs to observe the potential and limitations of TEDs for dataflow design verification. Application of TEDs to algorithmic and behavioral verification is demonstrated. [ABSTRACT FROM AUTHOR]

Recently, implementations of normal basis multiplication over the extended binary field GF(2m) have received considerable attention. A class of low complexity normal bases called Gaussian normal bases has been included in a number of standards, such as IEEE [1] and NIST [21 for an elliptic curve digital signature algorithm. The multiplication algorithms presented there are slow in software since they rely on bit-wise inner product operations. In this paper, we present two vector-level software algorithms which essentially eliminate such bit-wise operations for Gaussian normal bases; Our analysis and timing results show that the software implementation of the proposed algorithm is faster than previously reported normal basis multiplication algorithms. The proposed algorithm is also more memory efficient compared with its look-up table-based counterpart. Moreover, two new digit-level multiplier architectures are proposed and it is shown that they outperform the existing normal basis multiplier structures. As compared with similar digit-level normal basis multipliers, the proposed multiplier with serial output requires the fewest number of XOR gates and the one with parallel output is the fastest multiplier. [ABSTRACT FROM AUTHOR]

A Multiple Bus Network (MBN) connects a set of processors via a set of buses. Two important parameters of an MBN are its loading (largest number of connections on a bus) and its degree (largest number of connections to a processor). These parameters determine the cost, speed, and implementability of the MBN. The smallest degree that any useful MBN can have is 2. In this paper, we study the relationship between running time, degree, and loading of degree-2 MBNs running a fundamental class of algorithms called binary tree algorithms. (A binary tree algorithm reduces 2n inputs at the leaves of a balanced binary tree to a single result at the root of the tree.) Specifically, we establish a nontrivial Ω(n/log n) loading lower bound for any degree-2 MBN running a 2n input binary tree algorithm optimally in n steps. We show that this bound does not hold if the restriction on the degree or the running time is relaxed. That is, optimal-time, degree-3, constant loading MBNs and suboptimal-time, degree-2, constant loading MBNs exist for binary tree algorithms. We also derive a lower bound on the additional time (beyond the optimal) needed to run binary tree algorithms on a degree-2, loading-L MBN, for any L⩾ 3. [ABSTRACT FROM AUTHOR]