Look-ahead Algorithm Research Articles

Selective Sampling for Nearest Neighbor Classifiers

Most existing inductive learning algorithms work under the assumption that their training examples are already tagged. There are domains, however, where the tagging procedure requires significant computation resources or manual labor. In such cases, it may be beneficial for the learner to be active, intelligently selecting the examples for labeling with the goal of reducing the labeling cost. In this paper we present LSS—a lookahead algorithm for selective sampling of examples for nearest neighbor classifiers. The algorithm is looking for the example with the highest utility, taking its effect on the resulting classifier into account. Computing the expected utility of an example requires estimating the probability of its possible labels. We propose to use the random field model for this estimation. The LSS algorithm was evaluated empirically on seven real and artificial data sets, and its performance was compared to other selective sampling algorithms. The experiments show that the proposed algorithm outperforms other methods in terms of average error rate and stability.

The effects of look-ahead algorithms in content functional robotic intelligence

The last three years have shown a tremendous surge in interest in intelligent robotic systems. Real-time intelligence is of critical importance in areas such as space exploration and military opera...

Cluster-aware iterative improvement techniques for partitioning large VLSI circuits

Move-based iterative improvement partitioning (IIP) methods, such as the Fiduccia-Mattheyses (FM) algorithm [Fidducia and Mattheyses 1982] and Krishnamurthy's Look-Ahead (LA) algorithm [Krishnamurthy 1984], are widely used in VLSI CAD applications, largely due to their time efficiency and ease of implementation. This class of algorithms is of the "local/greedy improvement" type, and they generate relatively high-quality results for small and medium-size circuits. However, as VLSI circuits become larger, these algorithms suffer a rapid deterioration in solution quality. We propose new IIP methods CLIP and CDIP that select cells to move with a view to moving clusters that straddle the two subsets of a partition, into one of the subsets. The new algorithms significantly improve partition quality while preserving the advantage of time efficiency. Experimental results on 25 medium to large-size ACM/SIGDA benchmark circuits show up to 70% improvement over FM in mincut, and average mincut improvements of about 35% over all circuits and 47% over large circuits. They also outperform state-of-the-art non-IIP techniques, the quadratic-programming-based method Paraboli [Reiss et al. 1994] and the spectral partitioner MELO [Alpert and Yao 1995], by about 17% and 23%, respectively, with less CPU time. This demonstrates the potential of sophisticated IIP algorithms in dealing with the increasing complexity of emerging VLSI circuits. We also compare CLIP and CDIP to hMetis [Karypis et al. 1997], one of the best of the recent state-of-the-art partitioners that are based on the multilevel paradigm (others include ML c [Alpert et al. 1997] and LSR/MFFS [Cong et al. 1997]). The results show that one scheme of hMetis is 8% worse than CLIP/CDIP and the other two schemes are only 2--4% better. However, CLIP/CDIP have advantages over hMetis and other multilevel partitioners that outweigh these minimal mincut improvements. The first is much faster times-to-solution (for example, one of our best schemes CLIP-LA2 is 6.4 and 11.75 times faster than the two best hMetis schemes) and much better scalability with circuit size (e.g., for the largest circuit with about 162K nodes, CLIP-LA2 is 10.4 and and 21.5 times faster and obtains better solution qualities than the two best hMetis schemes). Second, CLIP/CDIP are "flat" partitioners, while multilevel techniques perform a sequence of node clustering/coarsening before partitioning the circuit. In complex placement applications such as timing-driven placement in the presence of multiple constraints, such circuit coarsening can hide crucial information needed for good-quality solutions, thus making the partitioning process oblivious to them. This, however, is not a problem with flat partitioners like CLIP/CDIP that can take all important parameters into account while partitioning. All these advantages make CLIP/CDIP suitable for use in complex physical design problems for large, deep-submicron VLSI circuits.

Partitioning using second-order information and stochastic-gain functions

A probability-based partitioning algorithm, PROP, was introduced in [8] that achieved large improvements over traditional "deterministic" iterative-improvement techniques like Fidducia-Mattheyses (FM) and Krishnamurthy's look-ahead (LA) algorithm. While PROP's gain function has a greater futuristic component than PM or LA, it incorporates spatially local information-only information on the removal probabilities of adjacent nets of a cell is used in its gain computation. This prevents a higher-level view of nonlocal structures. Also, giving uniform weights to all nets, results in an inability to differentiate between the futuristic benefit of removing one net from another. This paper investigates for the first time the issues of using nonlocal structural information in gain functions and variable net weights based on the futuristic (stochastic) benefit of moving them from the cutset. The result is a more sophisticated partitioner DEEP-PROP that performs better for circuits with large complexities by incorporating more nonlocal (second order) structural information than PROP. The second-order information is incorporated into cell gains as well as variable net weights-the latter helps to focus future cell moves in the "right" cluster around the currently moved cell and, thus, better utilizes the information that led to its selection as the best move. A lower complexity version, variable weight PROP (VAR-PROP), that also uses dynamically assigned variable net weights, but based on first-order information, has also been developed. Both versions yield significant improvements over PROP on the ACM/SIGDA benchmark suite. DEEP-PROP yields mincut improvements of as much as 39% and an average of 20% for large circuits (10-K to 25-K cells) and an average of 14% over all circuits. DEEP PROP is about a factor of 2.8 times slower than PROP, which is very fast. VAR-PROP, which has a much lower computational complexity than DEEP-PROP, yields for large circuits, maximum and average mincut improvements over PROP of 27% and 18%, respectively, and an average of 12.6% improvement over all circuits. It is only about 14% slower than PROP, For the only very large circuit golem3 in the suite (>100 K cells), the improvements produced by DEEP-PROP and VAR-PROP over PROP are 15.6% and 11.5%, respectively. We also compare DEEP-PROP to FM, PROP and hMetis for a subset of the newer 1SPD98 benchmark circuits, and demonstrate significant improvements over FM and PROP, and comparable mincuts (within 2%) to hMetis, one of the best multilevel partitioners.

Heuristics for Large Constrained Vehicle Routing Problems

This paper presents a heuristic for solving very large routing problems (thousands of customers and hundreds of vehicles) with side constraints such as time windows. When applied to traditional benchmarks (Solomon‘s), we obtain high quality results with short resolution time (a few seconds). We also introduce a LDS (Limited Discrepancy Search) variation that produces state-of-the-art results. The heart of this heuristic is a combination of a look-ahead insertion algorithm, an incremental local optimization scheme and a constraint solver for constrained traveling salesman problems. The incrementality means that instead of visiting some large neighborhood after an initial solution has been found, a limited number of moves is examined, after each insertion, on the partial solution. This incremental version is not only faster, it also yields better results than using local optimization once a full solution has been built. We also show how additional constraints can be used in order to guide the insertion process. Because of its use of separate CP (Constraint Programming) modules, this method is flexible and may be used to solve large dispatching problems that include many additional constraints such as setup times (asymmetrical distance) or skill matching.

No more “Partial” and “Full Looking Ahead”

Looking ahead is a commonly used search technique in constraint satisfaction. In this paper, we examine the future role of two long established lookahead algorithms, Partial Looking Ahead (PLA) and Full Looking Ahead (FLA). We prove that PLA is inferior to Directional Arcconsistency Lookahead in that the latter will prune at least as much as the former for no more computation in each problem reduction step. Similarly, FLA is inferior to Bi-directional Arcconsistency Lookahead, an algorithm introduced in this paper. We also point out a couple of errors in the literature.

Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations

In a recent paper, we introduced a new look-ahead algorithm for recursively computing Padé approximants. This algorithm generates a subsequence of the Padé approximants on two adjacent rows (defined by fixed numerator degree) of the Padé table. Its two basic versions reduce to the classical Levinson and Schur algorithms if no look-ahead is required. In this paper, we show that the computational overhead of the look-ahead steps in the O( N 2) versions of the look-ahead Levinson- and the look-ahead Schur-type algorithm can be further reduced. If the algorithms are used to solve Toeplitz systems of equations Tx = b , then the corresponding block LDU decompositions of T −1 or T , respectively, can be found with less computational effort than with any other look-ahead algorithm available today.

A lookahead algorithm for the solution of block toeplitz systems

We give a weakly stable algorithm to solve a block Toeplitz system of linear equations. If the lookahead steps taken to compute the parameters of the inversion formula for the block Toeplitz matrix are small compared to the order n of the matrix, the algorithm requires O( n 2) floating-point operations. The parameters of the inversion formula are interpreted and computed in a recursive way as solutions of certain interpolation problems given the formal Laurent series based on the data of the block Toeplitz matrix.

On Ramsey number R(4, 3, 3) and triangle-free edge-chromatic graphs in three colors

By applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two colorings of the edges of K 15 with three colors which do not contain a monochromatic triangle. Based on this result we derive a new upper bound for the three color Ramsey number, R(4, 3, 3) ⩽ 32. The best previously known bounds were 30⩽ R(4,3,3)⩽33.

Improved clustered look-ahead pipelining algorithm with minimum order augmentation

The author compares the overall performance of clustered look-ahead (CLA) filters with minimum order augmentation and scattered look-ahead (SLA) filters. To optimize the domain searching procedure and to improve the numerical performance, an improved CLA algorithm with minimum order augmentation, which is especially beneficial for high-Q high-speed digital filters, is proposed. This algorithm is optimized in the aspect of minimizing both the augmented pipelining order and undesirable quantization effects simultaneously. The proposed CLA structure with minimum order augmentation turns out to be very suitable for the applications that require high-speed and numerical stability.

Optimized look-ahead recurrences for adjacent rows in the Padé table

A new look-ahead algorithm for recursively computing Padé approximants is introduced. It generates a subsequence of the Padé approximants on two adjacent rows (defined by fixed numerator degree) of the Padé table. Its two basic versions reduce to the classical Levinson and Schur algorithms if no look-ahead is required. The new algorithm can be viewed as a combination of the look-ahead sawtooth and the look-ahead Levinson and Schur algorithms that we proposed before, but now the look-ahead step size is minimal (as in the sawtooth version) and the computational costs are as low as in the least expensive competing algorithms (including our look-ahead Levinson and Schur algorithms). The underlying recurrences link well-conditioned basic pairs,i.e., pairs of sufficiently different neighboring Padé forms. The algorithm can be used to solve Toeplitz systems of equationsTx = b. In this application it comes in several versions: anO(N 2) Levinson-type form, anO(N 2) Schur-type form, and a superfastO(N log2 N) Schur-type version. As an option of the first two versions, the corresponding block LDU decompositions ofT −1 orT, respectively, can be found.

Computation of Numerical Padé–Hermite and Simultaneous Padé Systems II: A Weakly Stable Algorithm

For $k+1$ power series $a_0(z), \ldots, a_k(z)$, we present a new iterative, look-ahead algorithm for numerically computing Pad\'{e}--Hermite systems and simultaneous Pad\'e systems along a diagonal of the associated Pad\'{e} tables. The algorithm computes the systems at all those points along the diagonal at which the associated striped Sylvester and mosaic Sylvester matrices are well conditioned. The operation and the stability of the algorithm is controlled by a single parameter $\tau$ which serves as a threshold in deciding if the Sylvester matrices at a point are sufficiently well conditioned. We show that the algorithm is weakly stable and provide bounds for the error in the computed solutions as a function of $\tau$. Experimental results are given which show that the bounds reflect the actual behavior of the error. The algorithm requires ${\cal O}(\|n\|^2 + s^3 \|n\|)$ operations to compute Pad\'{e}--Hermite and simultaneous Pad\'e systems of type $n=[n_0, \ldots, n_k]$, where $\|n\|=n_0+\cdots+n_k$ and $s$ is the largest step-size taken along the diagonal. An additional application of the algorithm is the stable inversion of striped and mosaic Sylvester matrices.

Formal Development of a Task-Oriented Look-Ahead Storage Management Scheme

The use of earliest-deadline-first task scheduling in hard real-time environments suggests as a by-product a method for hierarchical storage management, representing an application-specific implementation of the working set model. The algorithm presented essentially assigns storage to the ordered list of ready tasks provided by the scheduler. The scheme pages storage on the basis of entire tasks' code and data. Employing the knowledge available in real-time systems on future events leading to task (re-) activations, the look-ahead algorithm always replaces the page with the longest forward access distance. Hence, they are optimal as far as paging demands depend upon internally foreseeable events. In this paper a formal correctness proof using Hoare-style logic is worked out for this algorithm, HSA dmin . The task-oriented, look-ahead hierarchical storage administration scheme is part of an effort to develop a novel dependable and predictably behaving computer architecture for hard real-time environments featuring a fonnally specified and verified operating system kernel supporting an extended version of the high-level real-time programming language PEARL

Why do we need numerical methods for constrained fermion systems?

Approximative methods such as perturbation theory, mean-field caluclations or variational treatments are not reliable for many strongly interacting fermion models. Numerical methods are thus essential in the investigation of these strongly correlated fermion systems. A strong Coulomb repulsion present in these systems can often be replaced by a constraint to no-double occupancy, leading to an effective model for the low-energy excitations. These constrained systems are often easier to investigate. We review the “exact” algorithms mainly used to simulate constrained fermion systems, exact diagonalization, quantum Carlo and the quantum transfer matrix algorithm (QTM). We report on a new improved QTM algorithm, obtained by a combination of the QTM with the recently developed look-ahead Lanczos algorithm for non-hermitian matrices. These methods give reliable results and can answer many open questions in the field of strongly correlated electron systems.

A look-ahead heuristic for scheduling jobs with release dates on a single machine

The paper explores how limited look-ahead improves the performance of on-line heuristics. In particular, we consider the NP-complete single machine scheduling of independent jobs with release dates to minimize the total completion time. We present an on-line with look-ahead algorithm which foresees the next in-coming job. We study its worst-case behavior and prove that it outperforms most on-line and off-line heuristics.

An Implementation of the QMR Method Based on Coupled Two-Term Recurrences

Recently, the authors proposed a new Krylov subspace iteration, the quasi-minimal residual (QMR) algorithm, for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite-precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Some implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is proposed. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported.

A look-ahead algorithm for the solution of general Hankel systems

The solution of systems of linear equations with Hankel coefficient matrices can be computed with onlyO(n 2) arithmetic operations, as compared toO(n 3) operations for the general cases. However, the classical Hankel solvers require the nonsingularity of all leading principal submatrices of the Hankel matrix. The known extensions of these algorithms to general Hankel systems can handle only exactly singular submatrices, but not ill-conditioned ones, and hence they are numerically unstable. In this paper, a stable procedure for solving general nonsingular Hankel systems is presented, using a look-ahead technique to skip over singular or ill-conditioned submatrices. The proposed approach is based on a look-ahead variant of the nonsymmetric Lanczos process that was recently developed by Freund, Gutknecht, and Nachtigal. We first derive a somewhat more general formulation of this look-ahead Lanczos algorithm in terms of formally orthogonal polynomials, which then yields the look-ahead Hankel solver as a special case. We prove some general properties of the resulting look-ahead algorithm for formally orthogonal polynomials. These results are then utilized in the implementation of the Hankel solver. We report some numerical experiments for Hankel systems with ill-conditioned submatrices.

A look-ahead Levinson algorithm for general Toeplitz systems

The authors present an extension of Levinson's algorithm that is guaranteed to be weakly stable for a large class of general Toeplitz matrices, namely, those that do not have many consecutive ill-conditioned leading principal submatrices. The new algorithm adapts itself to the given Toeplitz matrix by skipping over all the ill-conditioned leading principal submatrices encountered during the solution process. This is done by a look-ahead strategy that monitors the condition of the leading principal submatrices and, if necessary, switches to a block step of suitable size. The overhead of the look-ahead algorithm is typically small compared to the classical Levinson algorithm, and in addition a reliable condition number estimate is produced.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Algorithm transformation techniques for concurrent processors

Progress in supercomputing technology has led to two major trends. First, many existing algorithms need to be redesigned for efficient concurrent implementation using supercomputers. Second, a continuous increase will be apparent in the number of application-specific VLSI integrated circuits, which can provide the performance of supercomputers using single chips or chipsets (at the expense of design time for algorithm and architecture development). Both of these approaches require considerable effort in the development of algorithms for specific applications. Four independent algorithm transformation methodologies-program unfolding, retiming, look-ahead algorithms, and index mapping transformations-are reviewed. These transformation techniques exploit the available parallelism in iterative data-flow programs and create additional parallelism if necessary. >

'DNA Strider': a 'C' program for the fast analysis of DNA and protein sequences on the Apple Macintosh family of computers.

DNA Strider is a new integrated DNA and Protein sequence analysis program written with the C language for the Macintosh Plus, SE and II computers. It has been designed as an easy to learn and use program as well as a fast and efficient tool for the day-to-day sequence analysis work. The program consists of a multi-window sequence editor and of various DNA and Protein analysis functions. The editor may use 4 different types of sequences (DNA, degenerate DNA, RNA and one-letter coded protein) and can handle simultaneously 6 sequences of any type up to 32.5 kB each. Negative numbering of the bases is allowed for DNA sequences. All classical restriction and translation analysis functions are present and can be performed in any order on any open sequence or part of a sequence. The main feature of the program is that the same analysis function can be repeated several times on different sequences, thus generating multiple windows on the screen. Many graphic capabilities have been incorporated such as graphic restriction map, hydrophobicity profile and the CAI plot- codon adaptation index according to Sharp and Li. The restriction sites search uses a newly designed fast hexamer look-ahead algorithm. Typical runtime for the search of all sites with a library of 130 restriction endonucleases is 1 second per 10,000 bases. The circular graphic restriction map of the pBR322 plasmid can be therefore computed from its sequence and displayed on the Macintosh Plus screen within 2 seconds and its multiline restriction map obtained in a scrolling window within 5 seconds.