Algorithm Schema Research Articles

Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS

In this paper, we present a general algorithmic schema called ‘Expand, Enlarge and Check’ from which new algorithms for the coverability problem of WSTS can be constructed. We show here that our schema allows us to define forward algorithms that decide the coverability problem for several classes of systems for which the Karp and Miller procedure cannot be generalized, and for which no complete forward algorithms were known. Our results have important applications for the verification of parameterized systems and communication protocols. A preliminary version of this paper has been published as [Geeraerts et al., Expand, enlarge and check: new algorithms for the coverability problem of WSTS, in: Proceedings of the 24th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 04), Lecture Notes in Computer Science, vol. 3328, Springer, Berlin, 2004, pp. 287–298] in the proceedings of FST&TCS 2004.

Library analysis of SCHEMA-guided protein recombination.

The computational algorithm SCHEMA was developed to estimate the disruption caused when amino acid residues that interact in the three-dimensional structure of a protein are inherited from different parents upon recombination. To evaluate how well SCHEMA predicts disruption, we have shuffled the distantly-related beta-lactamases PSE-4 and TEM-1 at 13 sites to create a library of 2(14) (16,384) chimeras and examined which ones retain lactamase function. Sequencing the genes from ampicillin-selected clones revealed that the percentage of functional clones decreased exponentially with increasing calculated disruption (E = the number of residue-residue contacts that are broken upon recombination). We also found that chimeras with low E have a higher probability of maintaining lactamase function than chimeras with the same effective level of mutation but chosen at random from the library. Thus, the simple distance metric used by SCHEMA to identify interactions and compute E allows one to predict which chimera sequences are most likely to retain their function. This approach can be used to evaluate crossover sites for recombination and to create highly mosaic, folded chimeras.

A schema for interprocedural modification side-effect analysis with pointer aliasing

The first interprocedural modification side-effects analysis for C (MOD C ) that obtains better than worst-case precision on programs with general-purpose pointer usage is presented with empirical results. The analysis consists of an algorithm schema corresponding to a family of MOD C algorithms with two independent phases: one for determining pointer-induced aliases and a subsequent one for propagating interprocedural side effects. These MOD C algorithms are parameterized by the aliasing method used. The empirical results compare the performance of two dissimilar MOD C algorithms: MOD C ( FSAlias ) uses a flow-sensitive, calling-context-sensitive interprocedural alias analysis; MOD C ( FIAlias uses a flow-insensitive, calling-context-insensitive alias analysis which is much faster, but less accurate. These two algorithms were profiled on 45 programs ranging in size from 250 to 30,000 lines of C code, and the results demonstrate dramatically the possible cost-precision trade-offs. This first comparative implementation of MOD C analyses offers insight into the differences between flow-/context-sensitive and flow-/context-insensitive analyses. The analysis cost versus precision trade-offs in side-effect information obtained are reported. The results show surprisingly that the precision of flow-sensitive side-effect analysis is not always prohibitive in cost, and that the precision of flow-insensitive analysis is substantially better than worst-case estimates and seems sufficient for certain applications. On average MOD C ( FSAlias ) for procedures and calls is in the range of 20% more precise than MOD C ( FIAlias ); however, the performance was found to be at least an order of magnitude slower than MOD C ( FIAlias ).

Using constraint metaknowledge to reduce arc consistency computation

Constraint satisfaction problems are widely used in artificial intelligence. They involve finding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the cost of consistency checking. In particular, such inferences can be used to reduce the number of constraint checks required in establishing arc consistency, a fundamental constraint-based reasoning technique. A general AC-Inference algorithm schema is presented and various forms of inference discussed. A specific algorithm, AC-7, is presented, which takes advantage of a simple property common to all binary constraints to eliminate constraint checks that other arc consistency algorithms perform. The effectiveness of this approach is demonstrated analytically, and experimentally.

Operations for Learning with Graphical Models

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, andthe manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximizationalgorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. The main original contributions here are the decompositiontechniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.

Improved approximations of independent sets in bounded-degree graphs via subgraph removal

Finding maximum independent sets in graphs with bounded maximum degree Δ is a well-studied NP-complete problem. We introduce an algorithm schema for improving the approximation of algorithms for this problem, which is based on preprocessing the input by removing cliques.We give an implementation of a theorem on the independence number of clique-free graphs, and use it to obtain an O(Δ/log log Δ) performance ratio with our schema. This is the first o(Δ) ratio for the independent set problem. We also obtain an efficient method with a Δ/6(1 + o(1)) performance ratio, improving on the best performance ratio known for intermediate values of Δ.

Analysis of parallel algorithms using pipeline architectures in computer vision applications

Recently a number of machine vision systems have been successfully implemented using pipeline architectures and various new algorithms have been proposed. In this paper we propose a method of analysis of both time complexity and space complexity for algorithms using conventional general purpose pipeline architectures. We illustrate our method by applying it to an algorithm schema for local window operations satisfying a property we define as decomposability. It is shown that the proposed algorithm schema and its analysis generalize previous published results. We further analyse algorithms implementing operators that are not decomposable. In particular the complexities of several median-type operations are compared and the implication on algorithm choice is discussed. We conclude with discussions on space-time trade-offs and implementation issues.

A practically efficient and almost linear unification algorithm

An efficient unification algorithm for first-order terms is described. It relies on the known theoretical framework of homogeneous and valid equivalence relations on terms and it makes use of a union-find algorithmic schema, thus keeping an almost linear worst-case complexity. Its advantages over similar algorithms are a very low overhead and practical efficiency, even for small terms, that are due to simple data structures and careful design tradeoffs. The proposed algorithm is described in detail such as to be easily implemented. Its main part is proved, and its complexity analyzed. Comparative experimental results that support its advantage are given.

Systolic structures: A notion and characterization

A notion of systolicity based on embeddability of processing structures is introduced. This notion characterizes the systolic structures that can be extended to solve problems of larger size, without a corresponding increase in processing time. A mathematical model for specifying such extendable structures is developed. The extensions of these structures are specified by extension rules using wavefronts and interconnection functions. An approach to deriving the algorithm schema corresponding to the computation performed by extendable structures is discussed. A simple necessary and sufficient condition for the systolicity of these structures is finally established.

A Family of Trust-Region-Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties

This paper has two aims: to exhibit very general conditions under which members of a broad class of unconstrained minimization algorithms are globally convergent in a strong sense, and to propose several new algorithms that use second derivative information and achieve such convergence. In the first part of the paper we present a general trust-region-based algorithm schema that includes an undefined step selection strategy. We give general conditions on this step selection strategy under which limit points of the algorithm will satisfy first and second order necessary conditions for unconstrained minimization. Our algorithm schema is sufficiently broad to include line search algorithms as well. Next, we show that a wide range of step selection strategies satisfy the requirements of our convergence theory. This leads us to propose several new algorithms that use second derivative information and achieve strong global convergence, including an indefinite line search algorithm, several indefinite dogleg algo...

Unstructured Mean Iterative Processes in Reflexive Banach Spaces

The unstructured mean iterative process is an algorithm schema that may be used to model numerical methods for solving fixed point problems. This schema relates the sequences $\{ {y_i } \}$ and $\{ {z_i } \}$ in a linear space X and a scalar sequence $\{ {\lambda _i } \}$ via the relation $z_{i + 1} = z_i + \lambda _i (y_i - z_i )$. The “unstructured” use of $y_i $ rather than the explicit use of an algorithmic map involving the iterates $z_i ,z_{i - 1} , \cdots ,z_0 $, allows the properties of the schema to be separated from the properties of any particular class of applications. The results presented concern the boundedness and convergence properties of $\{ {y_i } \}$ and $\{ {z_i } \}$ in reflexive Banach spaces, as controlled by the parameter sequence $\{ {\lambda _i } \}$. These properties provide guidelines that are useful in a systematic approach to the synthesis of the iterative algorithms for solving fixed point problems.

On a certain basis of operators and predicates with an undecidable emptiness problem

We shall consider algorithm schemata which are constructed from operators and predicates. Operators and predicates are assumed to be formal constructions which allow their interpretat ion as commands of an electronic computer. The class of schemata which we shall study are completely specified by the choice of a certain basis a set of operators and predicates from which the schemata are constructed. Problems of emptiness, inclusion and equivalence oriented on such a class of schemata are formulated as problems in the chosen basis.