An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significan

Robust Processing of Natural Language

Previous approaches to robustness in natural language processing usually treat deviant input by relaxing grammatical constraints whenever a successful analysis cannot be provided by ``normal'' means. This schema implies, that error detection always comes prior to error handling, a behaviour which hardly can compete with its human model, where many erroneous situations are treated without even noticing them. The paper analyses the necessary preconditions for achieving a higher degree of robustness in natural language processing and suggests a quite different approach based on a procedure for structural disambiguation. It not only offers the possibility to cope with robustness issues in a more natural way but eventually might be suited to accommodate quite different aspects of robust behaviour within a single framework.Comment: 16 pages, LaTeX, uses pstricks.sty, pstricks.tex, pstricks.pro, pst-node.sty, pst-node.tex, pst-node.pro. To appear in: Proc. KI-95, 19th German Conference on Artificial Intelligence, Bielefeld (Germany), Lecture Notes in Computer Science, Springer 199

On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

A Framework for Structured Quantum Search

A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to the underlying structure of abstract search spaces, and is analytically simpler than previous structured search methods. The algorithm is evaluated empirically with a variety of search problems, and shown to be particularly effective for searches with many constraints. Furthermore, the algorithm provides a simple framework for utilizing search heuristics. It also exhibits the same phase transition in search difficulty as found for sophisticated classical search methods, indicating it is effectively using the problem structure.Comment: 18 pages, Latex, 7 figures, further information available at ftp://parcftp.xerox.com/pub/dynamics/quantum.htm

An Approximately Optimal Algorithm for Scheduling Phasor Data Transmissions in Smart Grid Networks

In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure in the electric grid. The problem is cast in the framework of the classic job scheduling with precedence constraints. The optimization setup comprises the number of phasor measurement units (PMUs) to be installed on the grid, a weight associated with each PMU, processing time at the control center for the PMUs, and precedence constraints between the PMUs. The solution to the PMU placement problem yields the optimum number of PMUs to be installed on the grid, while the processing times are picked uniformly at random from a predefined set. The weight associated with each PMU and the precedence constraints are both assumed known. The scheduling problem is provably NP-hard, so we resort to approximation algorithms which provide solutions that are suboptimal yet possessing polynomial time complexity. A lower bound on the optimal schedule is derived using branch and bound techniques, and its performance evaluated using standard IEEE test bus systems. The scheduling policy is power grid-centric, since it takes into account the electrical properties of the network under consideration.Comment: 8 pages, published in IEEE Transactions on Smart Grid, October 201