CPU Time Consumption Research Articles

An improved version of ISICS: A program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The formatting of the M-shell atomic parameters imbedded in file XCSC.H in ISICS has been corrected. The problem only affected cross section calculations for Uranium and heavier elements. The corrected version of ISICS has been re-compiled and is now available. New version program summary Program title: ISICS Catalogue identifier: ADDS_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADDS_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4645 No. of bytes in distributed program, including test data, etc.: 106 731 Distribution format: tar.gz Programming language: C++ Computer: 80486 or higher-level PCs Operating system: WINDOWS 98 through WINDOWS XP Classification: 16.7 Does the new version supersede the previous version?: Yes Nature of problem: Ionization and X-ray production cross section calculations for ion-atom collisions. Solution method: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits. Reasons for new version: The formatting of the M-shell atomic parameters involving cross section calculations for Uranium and heavier elements needed to be corrected. Summary of revisions: The affected file XCSC.H in ISICS has been corrected and ISICS has been recompiled. Restrictions: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast. Running time: This depends on which shell and the number of different energies to be used in the calculation. For example, to calculate K-shell cross sections for protons striking carbon for 19 different proton energies it took less than 10 s; to calculate M-shell cross sections for protons on gold for 21 proton energies it took 4.2 min.

DIALIGN-TX: greedy and progressive approaches for segment-based multiple sequence alignment

BackgroundDIALIGN-T is a reimplementation of the multiple-alignment program DIALIGN. Due to several algorithmic improvements, it produces significantly better alignments on locally and globally related sequence sets than previous versions of DIALIGN. However, like the original implementation of the program, DIALIGN-T uses a a straight-forward greedy approach to assemble multiple alignments from local pairwise sequence similarities. Such greedy approaches may be vulnerable to spurious random similarities and can therefore lead to suboptimal results. In this paper, we present DIALIGN-TX, a substantial improvement of DIALIGN-T that combines our previous greedy algorithm with a progressive alignment approach.ResultsOur new heuristic produces significantly better alignments, especially on globally related sequences, without increasing the CPU time and memory consumption exceedingly. The new method is based on a guide tree; to detect possible spurious sequence similarities, it employs a vertex-cover approximation on a conflict graph. We performed benchmarking tests on a large set of nucleic acid and protein sequences For protein benchmarks we used the benchmark database BALIBASE 3 and an updated release of the database IRMBASE 2 for assessing the quality on globally and locally related sequences, respectively. For alignment of nucleic acid sequences, we used BRAliBase II for global alignment and a newly developed database of locally related sequences called DIRM-BASE 1. IRMBASE 2 and DIRMBASE 1 are constructed by implanting highly conserved motives at random positions in long unalignable sequences.ConclusionOn BALIBASE3, our new program performs significantly better than the previous program DIALIGN-T and outperforms the popular global aligner CLUSTAL W, though it is still outperformed by programs that focus on global alignment like MAFFT, MUSCLE and T-COFFEE. On the locally related test sets in IRMBASE 2 and DIRM-BASE 1, our method outperforms all other programs while MAFFT E-INSi is the only method that comes close to the performance of DIALIGN-TX.

Multilevel fast multipole algorithm for acoustic wave scattering by truncated ground with trenches

The multilevel fast multipole algorithm (MLFMA) is extended to solve for acoustic wave scattering by very large objects with three-dimensional arbitrary shapes. Although the fast multipole method as the prototype of MLFMA was introduced to acoustics early, it has not been used to study acoustic problems with millions of unknowns. In this work, the MLFMA is applied to analyze the acoustic behavior for very large truncated ground with many trenches in order to investigate the approach for mitigating gun blast noise at proving grounds. The implementation of the MLFMA is based on the Nystrom method to create matrix equations for the acoustic boundary integral equation. As the Nystrom method has a simpler mechanism in the generation of far-interaction terms, which MLFMA acts on, the resulting scheme is more efficient than those based on the method of moments and the boundary element method (BEM). For near-interaction terms, the singular or near-singular integrals are evaluated using a robust technique, which differs from that in BEM. Due to the enhanced efficiency, the MLFMA can rapidly solve acoustic wave scattering problems with more than two million unknowns on workstations without involving parallel algorithms. Numerical examples are used to demonstrate the performance of the MLFMA with report of consumed CPU time and memory usage.

Analysis of wall-function approaches using two-equation turbulence models

This paper focuses the attention on the drawbacks and abilities of wall-function techniques through an analysis of well-known wall-functions from literature. Besides this, some deeper analysis of these tools by means of physical and numerical considerations are carried out in order to improve their limitations when they are applied to predict heat transfer and fluid flow. Accuracy, grid-sensitivity, numerical behaviour and verification of numerical simulations are key aspects in this paper. The main purpose is to obtain tools which are able to predict both fluid flow and heat transfer with low CPU time consumption, reduced grid-sensitivity and a relatively good accuracy.

SMMP v. 3.0—Simulating proteins and protein interactions in Python and Fortran

We describe a revised and updated version of the program package SMMP. SMMP is an open-source FORTRAN package for molecular simulation of proteins within the standard geometry model. It is designed as a simple and inexpensive tool for researchers and students to become familiar with protein simulation techniques. SMMP 3.0 sports a revised API increasing its flexibility, an implementation of the Lund force field, multi-molecule simulations, a parallel implementation of the energy function, Python bindings, and more. Program summary Title of program:SMMP Catalogue identifier:ADOJ_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADOJ_v3_0.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Programming language used:FORTRAN, Python No. of lines in distributed program, including test data, etc.:52 105 No. of bytes in distributed program, including test data, etc.:599 150 Distribution format:tar.gz Computer:Platform independent Operating system:OS independent RAM:2 Mbytes Classification:3 Does the new version supersede the previous version?:Yes Nature of problem:Molecular mechanics computations and Monte Carlo simulation of proteins. Solution method:Utilizes ECEPP2/3, FLEX, and Lund potentials. Includes Monte Carlo simulation algorithms for canonical, as well as for generalized ensembles. Reasons for new version:API changes and increased functionality. Summary of revisions:Added Lund potential; parameters used in subroutines are now passed as arguments; multi-molecule simulations; parallelized energy calculation for ECEPP; Python bindings. Restrictions:The consumed CPU time increases with the size of protein molecule. Running time:Depends on the size of the simulated molecule.

Fast optimization method: the window size and hurst parameter estimator on self-similar network traffic

This paper describes a version of the Fast Optimization Method (FOM) used to estimate the Hurst parameter (H) with appropriate window sizes in self-similar network traffic. Large or short window sizes, for example, may cause the results to become unreliable. Estimating window sizes requires that the estimation process be repeated, such as in Iterative Optimization Method (IOM) and will result in the high consumption of CPU time. This paper empirically compares the CPU time and the estimation results using both the FOM and IOM methods. Finally, it shows that the FOM outperforms the IOM in that it significantly reduces total CPU time and maintains the reliability of the estimation results.

A Model to Optimize a Microwave PBG Accelerator Based on Generic Unit Cell

In this paper a numerical method, based on the well known Floquet–Bloch theory, useful to analyze the physical properties of a PBG based accelerator, is presented. The proposed model has been developed to analyze a 2D lattice characterized by a generic inclination angle between the two primitive translation vectors, thus resulting very useful when a periodic structure without an equilateral triangular or square cell has to be investigated. The numerical method has been optimized in order to account several number of space harmonics with a low CPU time and memory consumption. Comparisons with more complex numerical methods demonstrate the accuracy of our model. Several simulations have been performed to find all the geometrical parameters including the inclination angle of the unit cell, filling factor and index contrast. The proposed method, through an optimization procedure of the photonic band structure, allows to obtain a large spectral purity, high order mode suppression and high Q–values.

Improving the performance of the boundary element method with time‐dependent fundamental solutions by the use of a wavelet expansion in the time domain

AbstractThe object of this paper is a wavelet‐based formulation of the boundary element method (BEM) for diffusion problems, characterized by time‐dependent fundamental solution. While the BEM is a well known and often used technique, its time‐dependent formulation for diffusion problems is very rarely used in practical applications, due to the high computational cost which characterizes it. Here, a new formulation is proposed, which, through the use of the wavelet expansion of the time behaviour of the boundary elements, is characterized by a lower CPU time consumption when compared with the standard BEM diffusion formulation. The problem to be solved is transformed into an algebraic system (of higher dimension) and its solution gives the time domain behaviour of the desired quantities; in this way, the time stepping procedure is avoided. Together with the formulation, the analysis of the computational cost, and two examples are given in the paper. Copyright © 2006 John Wiley & Sons, Ltd.

An improved version of ISICS: a program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The C program, ISICS [Z. Liu, S.J. Cipolla, Comput. Phys. Comm. 97 (1996) 315–330], which calculates ionization and X-ray production cross-sections using PWBA and ECPSSR theory, has been enhanced to include new options, correct some minor flaws, and to make the program more versatile. Program summary Title of program: ISICS Catalog identifier: ADDS_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADDS_v2_0 Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: WINDOWS XP Program language used: C Computer: 80486 or higher-level PCs No. of lines in distributed program, including test data, etc.: 5343 No. of bytes in distributed program, including test data, etc.: 151 838 Distribution format: tar.gz Catalogue identifier of previous version: ADDS Journal reference of previous version: Comput. Phys. Comm. 97 (1996) 315–330 Does the new version supersede the previous version: Yes Nature of the physical problem: Ionization and X-ray production cross-section calculations for ion–atom collisions. Reasons for new version: Increased functionality and new options. Summary of revisions: Option for the united-atom approximation for binding-energy correction; easier inputting of updated atomic parameters; extension of projectile energy down to eV range; accounting for DHS wave function in K-shell ionization; other miscellaneous changes. Method of solution: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits. Restrictions on the complexity of the problem: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast. Typical running time: No change from previous version. Unusual features of the program: No

Application of the full-spectrum [formula omitted]-distribution method to photon Monte Carlo solvers

Accurate prediction of radiative heat transfer is key in most high temperature applications, such as combustion devices and fires. Among the various solution methods for the radiative transfer equation (RTE), the photon Monte Carlo (PMC) method is potentially the most accurate and the most versatile. The implementation of a PMC method in multidimensional inhomogeneous problems, however, can be limited by its demand for large computer storage space and its CPU time consumption. This is particularly true if the spectral absorption coefficient is to be accurately represented, due to its irregular behavior. On the other hand, the recently developed full-spectrum k-distribution (FSK) method reorders the irregular absorption coefficient into smooth k-distributions and, therefore, provides an efficient and accurate scheme for the spectral integration of radiative quantities of interest. In this paper the accuracy of the PMC method in solving the RTE and the efficiency and storage advantage provided by the FSK method are combined. The advantages of the proposed PMC/FSK method is described in detail. The accuracy and the efficiency of the method are demonstrated by sample calculations that consider inhomogeneous problems.

Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and Arnoldi–Chebyshev algorithm

An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi–Chebyshev method. This method preserves the banded structure sparsity of matrices of the algebraic eigenvalue problem and thus decreases memory use and CPU time consumption. The errors that affect computed eigenvalues and eigenvectors are due to the truncation in the discretization and to finite precision in the computation of the discretized problem. In this paper we analyze those two errors and the interplay between them. We use as a test case the 2D eigenvalue problem yielded by the computation of inertial modes in a spherical shell. This problem contains many difficulties that make it a very good test case. It turns out that single modes (especially most-damped modes i.e. with high spatial frequency) can be very sensitive to roundoff errors, even when apparently good spectral convergence is achieved. The influence of roundoff errors is analyzed using the spectral portrait technique and by comparison of double precision and extended precision computations. Through the analysis we give practical recipes to control the truncation and roundoff errors on eigenvalues and eigenvectors.

Device-partition method using equivalent-circuit model in three-dimensional device simulation

In this paper, the device-partition method (DPM) is proposed to improve the efficiency in 3-D device simulation. The idea of DPM is that a device is divided into several parts, and, therefore, the matrix solver only solves a part of the device at a time. In order to obtain the accurate solution, the iteration method is necessary in DPM. By the continuous iteration, we can obtain the accurate simulation results. PN diode and MOSFET are demonstrated using DPM in this paper. The comparison of simulation results between our simulator and 3-D Davinci device simulator is presented. The consumption of CPU time and memory is also discussed in this paper.

Closed-form Expressions for Layered Media Green's Functions That are Reliable Both in the Near Field and in the Far Field

The authors have developed an algorithm for the determination of accurate closed- form expressions of Green's functions for multilayered media. The algorithm is based on the fltting of the spectral domain Green's functions in terms of an asymptotic term plus a ratio of two polynomials. The fltting is carried out via the method of total least squares, which is a non-iterative method demanding very few computational resources. The resulting closed-form expressions for the Green's functions consist of a quasistatic term plus a sum of cylindrical waves. The quasistatic term provides the near-fleld behavior and the cylindrical waves provide the farfleld behavior. As a consequence of this, the closed-form expressions are very accurate irrespective of the distance between the source point and the observation point. DOI: 10.2529/PIERS060807124124 The application of the method of moments (MoM) to the solution of mixed potential integral equations (MPIE) has proven to be an e-cient numerical tool for the analysis of planar circuits and antennas (1). In fact, several commercial software products that are currently used in the design of planar structures (such as \Ansoft Ensemble, \Zeland IE3D, and \Agilent Momentum) are based on the solution of MPIE by means of the MoM. In order to solve the MPIE arising from the analysis of planar structures, it is necessary to calculate the Green's functions (GF) for the scalar and vector potentials in multilayered media. These GF can be determined via numerical computation of inflnite integrals that are commonly known as Sommerfeld integrals (SI). However, the highly-oscillatory nature of the integrands involved makes the numerical computation of SI cumbersome and time consuming (1). Some researches have developed speciflc techniques that make it possible to accelerate the nu- merical computation of SI (2,3). Unfortunately, these techniques have the drawback that they have to be repeatedly used every time the distance between the source and observation points changes. One technique for the computation of multilayered media GFs that has received much attention in the last flfteen years is the discrete complex image method (DCIM) (4). This technique makes it possible to obtain closed-form expressions of the GFs without requiring numerical integration. However, the closed-form expressions have been recently found to produce unpredictable errors in the far-fleld computation of the GFs (5). Although it is possible to raise the threshold value of the distance between source and observation points that marks the onset of numerical errors, this is achieved at the expense of a considerable CPU time consumption (5). The sensitivity of the DCIM to far-fleld numerical errors seems to decrease when a surface waves term is included in the closed-form expression of the GFs (4,6). Unfortunately, the surface-waves term contains poles of the spectral domain GFs as well as residues of the spectral domain GFs at these poles, and the accurate determination of both the poles and the residues requires time-consuming algorithms (6). Very recently, the rational function fltting method (RFFM) has been proposed as an alternative technique to DCIM for the determination of closed-form expressions of multilayered media GFs (7). In the new technique the GFs are expressed in terms of a quasistatic term plus a linear com- bination of cylindrical waves. The amplitudes and propagation constants of the cylindrical waves are obtained in the spectral domain by means of a vector fltting algorithm, which is an iterative algorithm. The main drawback of the RFFM is that the closed-form expressions for the GFs in- troduce unacceptable errors in the near-fleld (7). These errors are caused by the Hankel functions representing the cylindrical waves, and in particular, by the non-physical near-fleld singularities present in these Hankel functions. In this paper, we present a revised version of the RFFM which substantially improves the original approach published in (7). In one hand, the determination of

An enhanced version of SMMP—open-source software package for simulation of proteins

We describe a revised and updated version of the program package SMMP ( Simple Molecular Mechanics for Proteins) [F. Eisenmenger, U.H.E. Hansmann, Sh. Hayryan, C.-K. Hu, Comput. Phys. Comm. 138 (2001) 192–212]. SMMP is an open-source FORTRAN package for molecular simulation of proteins within the standard geometry model. It is designed as a simple and inexpensive tool for researchers and students to become familiar with protein simulation techniques. This announcement describes the first major revision of this software package and its newly added features. Program summary Title of program:SMMP Catalogue identifier:ADOJ −v2 −0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADOJ_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested:LINUX system Programming language used:FORTRAN Computer:PC Pentium Number of lines in distributed program, including test data, etc.:18 492 Number of bytes in distributed program, including test data, etc.:278 995 Distribution format:ASCII Card punching code:ASCII Catalogue Identifier of previous version:ADOJ Journal Reference of previous version:F. Eisenmenger, U.H.E. Hansmann, Sh. Hayryan, C.-K. Hu, Comput. Phys. Comm. 138 (2001) 192–212 Does the new version supersede the previous version?:Yes Nature of physical problem:Molecular mechanics computations and Monte Carlo simulation of proteins Reasons for the new version:Increased functionality Summary of revisions:Changes in energy function and protein representation; differences in program structure and organization; new functionalities added; miscellaneous changes and additions Method of solution:Utilizes ECEPP2/3 and FLEX potentials. Includes Monte Carlo simulation algorithms for canonical, as well as for generalized ensembles Restrictions on the complexity of the problem:The consumed CPU time increases with the size of protein molecule Typical running time:Depends on the size of the molecule under simulation Unusual features of the program:No

Fast Structure-Based Virtual Ligand Screening Combining FRED, DOCK, and Surflex

A protocol was devised in which FRED, DOCK, and Surflex were combined in a multistep virtual ligand screening (VLS) procedure to screen the pocket of four different proteins. One goal was to evaluate the impact of chaining "freely available packages to academic users" on docking/scoring accuracy and CPU time consumption. A bank of 65 660 compounds including 49 known actives was generated. Our procedure is successful because docking/scoring parameters are tuned according to the nature of the binding pocket and because a shape-based filtering tool is applied prior to flexible docking. The obtained enrichment factors are in line with those reported in recent studies. We suggest that consensus docking/scoring could be valuable to some drug discovery projects. The present protocol could process the entire bank for one receptor in less than a week on one processor, suggesting that VLS experiments could be performed even without large computer resources.

A methodology for the coupling of RAMONA-3B neutron kinetics and TRAC-BF1 thermal-hydraulics

The initial objective of this project was to directly couple the RAMONA and TRAC codes running on different PCs. The idea was to use the best part of each one and eliminate some of their limitations and widen the applicability of these codes to simulate different BWR and system components. It was required to try to minimize the amount of changes to present code subroutines and calculation procedures. If possible, just substitute values obtained in the parallel code. Preliminary results indicated that using a CHAN component of TRAC to model thermal-hydraulic phenomena for each neutronic channel modeled in RAMONA is rather difficult. Large amounts of CPU time consumption are obtained and lots of PCs would make this solution difficult, besides considerable large transients are introduced by the differences in thermal-hydraulic results of these codes. The substitution of the thermal-hydraulics of RAMONA, by the TRAC channel calculations, is possible but simulation of a null transient on both codes must be planed and a gradual change must be controlled by an additional supervisory subroutine. An indirect coupling of these codes, it is therefore proposed, in order to eliminate most of these limitations. In this indirect coupling, a thermal-hydraulic model of the average tube in a bundle and the global channel cooling fluid dynamics is programmed for each neutronic channel while the global reactor vessel and core is modeled by TRAC with just four channels and four rings. Results are more reliable, coupling is simpler and faster simulations are possible.

State-of-the-Art of the Windowing Technique

Abstract The windowing technique was first introduced by Heinemann and Deimbacher(1) in 1993. This method allows a locally restricted and time-dependent replacement of grids and parameters during simulation runs. Windows can represent any area of special interest in a reservoir. In most cases, this is the near wellbore area, for the purpose of resolving near wellbore effects. By applying the 3D (k-)PEBI gridding(2) method, grids for arbitrary trajectories ofadvanced wells that resolve the near wellbore area and the wellbore itself can be generated. To handle detailed grids in full scale models, the timestep length must be drastically reduced. Therefore, these grids can only be used efficiently if the solution of the equations for the full, coarse model and the refined area is separated. This can be done based on a special kind of domain decomposition, which forms the theoretical basis of the windowing technique. Besides well modelling, the windowing technique has many other applications. Keeping overall CPU time consumption in the order of magnitude of a conventional model, the windowing technique is not only a potential approach to replace the analytical Peaceman model(3) in full field reservoir simulation, but also can be used for efficient well test simulation or dynamic flow based gridding. This paper presents the state-of-the-art of current window gridding techniques and their solution methodologies. Several examples to demonstrate the advantages of this tool for detailed and full field reservoir simulation are included. Introduction Special treatment and high resolution of regions of interest, both in time and space, have always been important issues in reservoir simulation. Several techniques have been developed in the past in attempting to solve the CPU efficiency problem in the application of local grid refinement, including patch refinement, true refinement, or multigrid methods(4–8). None of these techniques could fully satisfy the requirements of local grid replacement by flexible and irregular grids and its time dependent incorporation in full field reservoir simulation. The concept of the windowing and local timestepping technique was first introduced by Heinemann and Deimbacher in 1993(9–11). Application and further developments of the windowing technique proved it to be a multi-purpose numerical tool for a wide range of applications for simulation problems, including ell modelling in full field reservoir simulation and flow based gridding. Since its first publication, the technique has undergone several modifications. The purpose of this paper is to present the methodology in its current form and to give a coherent picture of the state-of-the-art of its application. Therefore, we first summarize the window solution methodology as it is implemented to date. Then the technique is validated using a small coning example. Finally, the state-of-the-art of its application, both from a gridding and simulation perspective, including well modelling, well test simulation, and flow based gridding, will be presented.

Hydrodynamic parameters of hydrated macromolecules: Monte Carlo calculation

A theoretical model for computing the basic hydrodynamic parameters of macromolecules in a water environment is presented. Starting from the 3D structure of the molecule, taking into account the hydration shell, the following parameters are calculated: translation friction coefficient, diffusion coefficient and intrinsic viscosity. The novel Monte Carlo algorithms also work effectively in the case of large molecules. The consumption of CPU time is proportional to Nq, where N is the number of atoms in the molecule and q a coefficient of 1.6–1.7, respectively.

A NOVEL SEGREGATED ALGORITHM FOR INCOMPRESSIBLE FLUID FLOW AND HEAT TRANSFER PROBLEMS—CLEAR (COUPLED AND LINKED EQUATIONS ALGORITHM REVISED) PART II: APPLICATION EXAMPLES

In Part I of this article a novel algorithm, CLEAR, was introduced. In this article the relative performance of the CLEAR algorithm and the SIMPLER algorithm is evaluated for six incompressible fluid flow and heat transfer problems with constant property. The six examples cover three two-dimensional orthogonal coordinates. Comprehensive comparisons are made between the two algorithms on the subject of iteration number for obtaining a converged solution, and the consumed CPU time. It is found that CLEAR can appreciably enhance the convergence rate. For the six problems tested, the ratio of iteration numbers of CLEAR over that of SIMPLER ranges from 0.15 to 0.84, and the ratio of the CPU time from 0.19 to 0.92.

Increasing feasibility of optimal gene network estimation.

Disentangling networks of regulation of gene expression is a major challenge in the field of computational biology. Harvesting the information contained in microarray data sets is a promising approach towards this challenge. We propose an algorithm for the optimal estimation of Bayesian networks from microarray data, which reduces the CPU time and memory consumption of previous algorithms. We prove that the space complexity can be reduced from O(n(2) x 2(n)) to O(2(n)), and that the expected calculation time can be reduced from O(n(2) x 2(n)) to O(n x 2(n)), where n is the number of genes. We make intrinsic use of a limitation of the maximal number of regulators of each gene, which has biological as well as statistical justifications. The improvements are significant for some applications in research.