Showing papers on "Probabilistic analysis of algorithms published in 1981"

A comparative study of several dynamic time-warping algorithms for connected-word recognition

Abstract: Several different algorithms have been proposed for time registering a test pattern and a concatenated (isolated word) sequence of reference patterns for automatic connected-word recognition. These algorithms include the two-level, dynamic programming algorithm, the sampling approach and the level-building approach. In this paper, we discuss the theoretical differences and similarities among the various algorithms. An experimental comparison of these algorithms for a connected-digit recognition task is also given. The comparison shows that for typical applications, the level-building algorithm performs better than either the two-level DP matching or the sampling algorithm.

A new algorithm for factoring polynomials over finite fields

Abstract: in F[t]. There are two standard methods; one is due to E. Berlekamp, the other appears to be a "folk method". Both are described by D. Knuth in [3, pp. 381-397]. Further improvements, for special values of q, are given by R. Moenck in [5J. See also E. Berlekamp [1]. (Note that both methods as described in the references apply only when d = 1, however, straightforward modifications, described below, allow d > 1.) Both methods use the calculation of resultants (or equivalently the solution of linear equations) to reduce the problem to finding the roots of a polynomial which has all of its roots in F. When p is very small, probabilistic methods are used. An improvement to the "folk method" method, along with a more explicit calculation of the work required, has recently been given by M. Rabin [6]. We present here a new probabilistic method which, when combined with the above algorithms, avoids the need for both resultants and linear equations. It leads to algorithms which are conceptually simpler than previous methods. Moreover, it works equally well for all finite fields F, regardless of the magnitude of q. When used for factoring a quadratic x2 a, it reduces to Berlekamp's algorithm. Other standard algorithms for factoring quadratics are due to D. H. Lehmer [4] and D. Shanks [7]. Our algorithm is also suitable for finding solutions of polynomial equations over finite fields.

Fast, Efficient Parallel Algorithms for Some Graph Problems

Abstract: Algorithms for solving graph problems on an unbounded parallel model of computation are considered. Parallel algorithms of time complexity $O(\log ^2 n)$ are described for finding biconnected components, bridges, minimum spanning trees and fundamental cycles. In the algorithms for finding minimum spanning trees, bridges, and fundamental cycles, the number of processors used is small enough that the parallel algorithm is efficient in comparison with the best sequential algorithms for these problems. Several other algorithms are presented which are especially suitable for processing sparse graphs.

Symmetry breaking in distributive networks

Abstract: Given a ring (cycle) of n processes it is required to design the processes so that they will be able to choose a leader (a uniquely designated process) by sending messages along the ring. If the processes are indistiguishable there is no deterministic algorithm, and therefore probabilistic algorithms are proposed. These algorithms need not terminate, but their expected complexity (time or number of bits of communication) is bounded by a function of n. If the processes work asynchronously then on the average O(n log2n) bits are transmitted. In the above cases the size n of the ring was assumed to be known. If n is not known it is suggested first to determine the value of n and then use the above algorithm. However, n may only be determined probabilistically and any algorithm may yield an incorrect value. In addition, it is shown that the size of the ring cannot be calculated by any probabilistic algorithm in which the processes can sense termination.

Characterization and evaluation of uncertainty in probabilistic risk analysis

Abstract: The sources of uncertainty in probabilistic risk analysis are discussed, using the event and fault-tree methodology as an example. The role of statistics in quantifying these uncertainties is investigated. A class of uncertainties is identified which are, at present, unquantifiable using either classical or Bayesian statistics. it is argued that Bayesian statistics is the more appropriate vehicle for the probabilistic analysis of rare events, and a short review is given with some discussion on the representation of ignorance.

Relationships between Probabilistic and Deterministic Tape Complexity

Abstract: By giving a matrix inversion algorithm that uses a small amount of space, a result of Simon is improved: For constructible functions f(n)∉ o(logn) f(n) tape-bounded probabilistic Turing machines can be simulated on deterministic ones within (f(n))2 space.

Linear cost is sometimes quadratic

Abstract: In analysis of programs and many other kinds of computation, algorithms are commonly written to have an input P and an output Q, where both P and Q are large and complicated objects. For example, P might be a routing problem and Q might be a solution to P. Although documented and discussed in this exhaustive style, algorithms are sometimes intended for use in contexts with two departures from the one-time analysis of an entire new input. First, the current value of P is the result of a small change to a previous value of P. We want to update the results of the previous analysis without redoing all of the work. Second, accurate information is only wanted in some designated portion of the large output Q. Possibly inaccurate information may appear elsewhere in Q. We want the analysis to be demand-driven: accurate where accuracy is demanded, but not burdened by the cost of providing much more than is demanded. This paper studies demand-driven algorithms capable of updating without extensive reanalysls. Such algorithms are called incremental, in contrast with the one-time analysis of an entire new input contemplated by exhaustive algorithms. In some cases, it is shown that an exhaustive algorithm can be easily recast in an efficient incremental style. Other algorithms for the same problem may be much less amenable to incremental use. It is shown that traditional exhaustive computational complexity bounds are poor predictors of incremental performance. The main examples are taken from global data flow analysis.

Performance analysis of high-speed digital buses for multiprocessing systems

Abstract: Current multiprocessing systems are often organized by connecting several devices with similar characteristics (usually processors) to a common bus. These devices present access with minimal delay; access is controlled by the bus arbitration algorithm. This paper presents a probabilistic analysis of several arbitration algorithms according to several criteria that reflect their relative performances in (1) rendering equal service to all competing devices and (2) allocating available bus bandwidth efficiently. The sensitivity of these criteria to the number of devices on the bus, the speed of the bus, and the distribution of interrequest times is considered.A probabilistic model for the quantitative comparison of these algorithms is constructed in which multiple devices repeatedly issue bus requests at random intervals according to an arbitrary distribution function and are serviced according to one of the algorithms; the devices do not buffer bus requests. The algorithms studied include the static priority, fixed time slice (FTS), two dynamic priority, and first-come, first-served (FCFS) schemes. The performance measures are computed by simulation. The analysis reveals that under heavy bus loads, the dynamic priority and FCFS algorithms offer significantly better performances by these measures than do the static priority and FTS schemes.

Distributed algorithms for synchronizing interprocess communication within real time

Abstract: This paper considers a fixed (possibly infinite) set π of distributed asynchronous processes which at various times are willing to communicate with each other. We describe probabilistic algorithms for synchronizing this communication with boolean “flag” variables, each of which can be written by only one process and read by at most one other process. With very few assumptions (the speeds of processes may vary in time within fixed arbitrary bounds, and the processes may be willing to communicate with a time varying set of processes (but bounded in number), and no probability assumptions about system behavior) we show our synchronization algorithms have real time response: If a pair of processes are mutually willing to communicate within a constant time interval, they establish communication in that interval, with high likelihood (for the worst case behavior of the system). Our communication model and synchronization algorithms are quite robust. They are applied to solve a large class of real time resource synchronization problems, as well as real time implementation of the synchronization primitives of Hoare's multiprocessing language CSP.

Complexity of algorithms and computations

Abstract: A survey is given of some results on the complexity of algorithms and computations published up to 1973.

Probabilistic methods for dynamic analysis of floating bridges

Abstract: Probabilistic methods for dynamic analysis of floating bridges exposed to short-crested sea waves are presented. The sea surface is idealized as a three-dimensional zero mean ergodic Gaussian field from which the wave loading process is derived using linear potential theory. The structural idealization is based on the finite element method. Structural response is obtained both in the frequency domain using the spectral approach and in the time domain by a sample path approach using Monte Carlo simulation. To exemplify the theory, results are presented for a 1200 metre long, continuous curved floating bridge. The report contains the paper presented at "European Simulation Meeting, Modelling and Simulation of Large-Scale Structural Systems", Capri, Italy, September 24-25, 1981. (Author/TRRL)

A model of recognition algorithms with representative samples and systems of supporting sets

Abstract: A class of recognition algorithms based on a mixed principle is described: in the construction the basic ideas of both algorithms of “Kora” type and also algorithms of the calculation of estimates are used.

Probabilistic and hazard analysis for pore pressure increase in soils due to seismic loading

Abstract: This research is primarily concerned with the evaluation of the likelihood of pore pressure build-up during an earthquake. As part of a long-term project, the report reviews methods for pore pressure development and liquefaction and documents and investigates the behavior of cohesionless soils in cyclic loading. Described are the development and application of a probabilistic pore pressure model using laboratory data; the probabilistic development of pore pressure using an effective stress model; and a probabilistic pore pressure analysis and seismic hazard evaluation. A generalized methodology is presented. Recommendations for future work include the improvement and application of the models and specific research tasks for completion of the methodology. The models developed in this study are shown to be advantageous over conventional methods.

Probabilistic evaluation of loads

Abstract: The loads that affect geotechnical designs are reviewed, characterizing the uncertainties in each load component. Probabilistic models for evaluating each component are examined. Whenever data are available, the level of variabilities and uncertainties associated with the effect of each component on the foundation is assessed. Satisfactory performance of a geotechnical system relies, in part, on a good understanding of the characteristics of the loads and environments to which the system is subjected. Uncertainties do exist in these factors. For dynamic loads due to earthquake excitation and wave action, both their magnitude and frequencies of occurrences over the expected duration of the system could not be known. The long-term stability of soil slope would also be dependent on stochastic fluctuation of the pore pressure due to seasonal variation and other temporal changes in the environment. (ASCE)

Note on probabilistic algorithms in integer and polynomial arithmetic

Abstract: For many computational problems it is not known whether verification of a result can be done faster than its computation. For instance, it is unknown whether the verification of the validity of the integer equality x*y=z needs fewer bit operations than a computation of the product x*y. It is sometimes much easier, however, to speed up the computation probabilistically if just the verification of the result is involved.In this paper we present linear probabilistic algorithms for verification of the validity of the integer equality f1(x1,...,xN)=f2(x1,...,xN) for rational functions f1 and f2, which can be of the form of a rational combination of rational functions.

Probabilistic stability analysis of gravity platforms

Abstract: A probabilistic model is proposed for evaluating the variation of stability risks over time after platform installation. A Bayesian procedure is formulated to update the statistics of the consolidation parameters from settlement measurements, and reevaluate the probability of foundation failure in subsequent years. A case study is used to demonstrate the proposed methodology. For the covering abstract of the conference see TRIS no 450958.

Short-term reliability of slopes under static and seismic conditions

Abstract: A simplified probabilistic approach to the determination of the short-term (phi sub u = 0) reliability of clayey slopes under static and seismic conditions is presented. The uncertainties associated with (a) the undrained strength of soil and its spatial variation and (b) the analytic procedure used to assess the safety of the slope are considered, and probabilistic tools are introduced for their description and amelioration. The probability of the failure of a slope under static loading is first determined. The effect of an earthquake on the slope is introduced through an equivalent horizontal peak acceleration (deterministic), and the new probability of failure is obtained by using Bayes' theorem. Finally, the developed procedure is illustrated in an example, the results of which are presented and discussed. (Author)

Algorithms with Random Input

Abstract: Randomness arises in connection with algorithms and their analysis in at least two different ways, Some algorithms (sometimes called coin-flipping algorithms) provide their own randomness, perhaps through the use of random number generators, Sometimes, though, it is useful to analyze the performance of a deterministic algorithm under some assumption about the distribution of inputs, We briefly survey some work which gives a perspective on such problems, Next we discuss some of the techniques which are useful when carrying out this type of analysis, Finally, we briefly discuss the problem of choosing an appropriate distribution

Synthesis of a class of fixed point algorithms: The deterministic case

Abstract: a solution of the given problem. For brevity, we refer to this as a convergent algorithm. Some of the properties needed to show that a fixed-point algorithm is convergent depend directly on the fixed-point formulation. Other properties that are needed to show convergence may depend more on some alternate reformulation. For example, many fixedpoint problems can be rewritten as potential function problems in which the solution set minimizes some potential function. The convergence theory of algorithms for minimizing potential functions has received considerable attention [6, 7 , 8 , 15, 231, but some of the conditions that are prerequisite to this theory are not of a constructive nature. Some of our results remedy this for a class of fixed-point algorithms.

Statistical aspects of design: risk assessment and structural integrity

Abstract: Statistical variations in input parameters that affect structural reliability have historically been incorporated approximately in engineering designs by application of safety factors. Increased concerns over the injury potential and costs of licensing, insurance, field repairs or recalls, and product liability claims now demand more quantitative evaluation of possible flaws or unusual usage conditions that might result from statistical variations or uncertainties. This paper describes the basic concepts of probabilistic fracture mechanics that are used to assess and control risk. Recent developments in combined analysis methods are presented that utilize field experience data with probabilistic analysis to improve the accuracy of the structural integrity predictions. Several specific examples are described that illustrate how these probabilistic methods are used to assess risk and to provide a quantitative basis for establishing design, operation or maintenance allowables. These procedures, which realistically model the actual statistical variations that exist, can eliminate unnecessarily conservative approximations and often achieve improved reliability at reduced cost.