2938206
An Optimal Parallel Algorithm for Formula Evaluation
A new approach to Buss’s ${\textbf{NC}}^1 $ algorithm [Proc. 19th ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123–131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for ${\textbf{NC}}^1 $ over ${\textbf{AC}}^0 $ reductions. This approach is then used to solve the more general problem of evaluating arithmetic formulas by using arithmetic circuits.
42435460
Embeddings of k-connected graphs of pathwidth k
We present O(n^3) embedding algorithms (subgraph isomorphism and its generalizations) for classes of graphs of bounded pathwidth, where n is the number of vertices in the graph. These include the first polynomial-time algorithm for minor containment and the first O(n^c) algorithm (c a constant independent of k) for topological embedding of graphs from subclasses of partial k-trees, as well as an O(n^2) algorithm for subgraph isomorphism. Of independent interest are structural properties of k-connected graphs of bounded pathwidth on which our algorithms are based. We also describe special cases which reduce to various generalizations of string matching, permitting more efficient solutions. Finally, we describe n^k^+^O^(^1^) algorithms for solving these problems on arbitrary graphs of pathwidth at most k.
204999323
Acyclic Directed Hypercubes may have Exponential Diameter
Abstract The diameter of a directed graph is the maximum of the lengths of the shortest paths between all pairs of vertices (if such paths exist). We prove that for every n , the edges of the n -dimensional hypercube can be acyclically oriented such that the diameter of the cube is F n + 1 , the ( n + 1)st Fibonacci number.
17058061
Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees
We present sequential and parallel algorithms for various embedding problems on bounded degree partial k-trees and k-connected partial k-trees; these include subgraph isomorphism and topological embedding, known to be NP-complete for general partial k-trees. As well as contributing to our understanding of the types of graphs for which these problems are tractable, this paper introduces methods for solving problems on graphs. In particular, we make use of the tree-decomposition of the graph to apply techniques used to solve problems on trees to solve problems on partial k-trees.
209133
Computing planar intertwines
The proof of Wagner's conjecture by N. Robertson and P. Seymour gives a finite description of any family of graphs which is closed under the minor ordering, called the obstructions of the family. Since the intersection and the union of two minor closed graph families are again a minor closed graph family, an interesting question is that of computing the obstructions of the new family given the obstructions for the original two families. It is easy to compute the obstructions of the intersection, but, until very recently, it was an open problem to compute the obstructions of the union. It is shown that if the original families are planar, then the obstructions of the union are no larger than n to the O(n/sup 2/) power, where n is the size of the largest obstruction of the original family.<<ETX>>
38885821
Embeddings of k-Connected Graphs of Pathwidth k
We present O(n3) embedding algorithms (generalizing subgraph isomorphism) for classes of graphs of bounded pathwidth, where n is the number of vertices in the graph. These include the first polynomialtime algorithm for minor containment and the first O(nc) algorithm (c a constant independent of k) for topological embedding of graphs from subclasses of partial k-trees. Of independent interest are structural properties of k-connected graphs of bounded pathwidth on which our algorithms are based. We also describe special cases which reduce to various generalizations of string matching, permitting more efficient solutions.
14760800
Deciding Separation Logic Formulae by SAT and Incremental Negative Cycle Elimination
Separation logic is a subset of the quantifier-free first order logic. It has been successfully used in the automated verification of systems that have large (or unbounded) integer-valued state variables, such as pipelined processor designs and timed systems. In this paper, we present a fast decision procedure for separation logic, which combines Boolean satisfiability (SAT) with a graph based incremental negative cycle elimination algorithm. Our solver abstracts a separation logic formula into a Boolean formula by replacing each predicate with a Boolean variable. Transitivity constraints over predicates are detected from the constraint graph and added on a need-to basis. Our solver handles Boolean and theory conflicts uniformly at the Boolean level. The graph based algorithm supports not only incremental theory propagation, but also constant time theory backtracking without using a cumbersome history stack. Experimental results on a large set of benchmarks show that our new decision procedure is scalable, and outperforms existing techniques for this logic.
8920735
Partition-based decision heuristics for image computation using SAT and BDDs
Methods based on Boolean satisfiability (SAT) typically use a conjunctive normal form (CNF) representation of the Boolean formula, and exploit the structure of the given problem through use of various decision heuristics and implication methods. We propose a new decision heuristic based on separator-set induced partitioning of the underlying CNF graph. It targets those variables whose choice generates clause partitions with disjoint variable supports. This can potentially improve performance of SAT applications by decomposing the problem dynamically within the search. In the context of a recently proposed image computation method combining SAT and BDDs, this results in simpler BDD subproblems. We provide algorithms for CNF partitioning - one based on a clause-variable dependency matrix, and another based on standard hypergraph partitioning techniques, and also for the use of partitioning information in decision heuristics for SAT. The effectiveness of the proposed partition-based heuristic is shown with practical results for reachability analysis of benchmark sequential circuits.
40714150
A semantic mediation approach for problems in computational molecular biology
As great amount of data are being produced and accumulated in life sciences, information access and consequent integration in analytical and computational methods become critical issues in order to conduct research. In this work we describe how the synergic combination of a high-level programmable planner engine and formal semantics are suitable to resolve many information integration problems in molecular biology.
11198288
Why the Information Explosion Can Be Bad for Data Mining, and How Data Fusion Provides a Way Out
One may claim that the exponential growth in the amount of data provides great opportunities for data mining. Reality can be different though. In many real world applications, the number of sources over which this information is fragmented grows at an even faster rate, resulting in barriers to widespread application of data mining and missed business opportunities. Let us illustrate this paradox with a motivating example from database marketing. In marketing, direct forms of communication are becoming increasingly popular. Instead of broadcasting a single message to all customers through traditional mass media such as television and print, the most promising potential customers receive personalized offers through the most appropriate channels. So it becomes more important to gather information about media consumption, attitudes, product propensity etc. at an individual level. Basic, company specific customer information resides in customer databases, but market survey data depicting a richer view of the customer are only available for a small sample or a disjoint set of reference customers. Collecting all this information for the whole customer database in a single source survey would certainly be valuable but is usually a very expensive proposition. The common alternative within business to
1782369
Designing and executing scientific workflows with a programmable integrator
MOTIVATION
As in many other fields of science, computational methods in molecular biology need to intersperse information access and algorithm execution in a computational workflow. Users often find difficulties when transferring data between data sources and applications. In most cases there is no standard solution for workflow design and execution and tailored scripting mechanisms are implemented in a case by case basis.


RESULTS
In this paper, we present a general purpose 'programmable integrator' that can access information from a variety of sources in a coordinated manner. Its usefulness in complex bioinformatics applications is claimed and supported by some application examples.


AVAILABILITY
Tools are freely available to non-profit educations and research institutions. Usage by commercial organizations requires a license agreement. Software requirements: Java v1.3 (http://java.sun.com), Xerces XML Parser (http://xml.apache.org/xerces-j) and Kweelt implementation of XQuery (http://kweelt.sourceforge.net/).