Pattern backtracking algorithm for the workflow satisfiability problem with user-independent constraints

The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment. (Such an assignment is called valid.) The problem is NP-hard even when restricted to the large class of user-independent constraints. Since the number of steps k is relatively small in practice, it is natural to consider a parametrisation of the WSP by k. We propose a new fixed-parameter algorithm to solve the WSP with user-independent constraints. The assignments in our method are partitioned into equivalence classes such that the number of classes is exponential in k only. We show that one can decide, in polynomial time, whether there is a valid assignment in an equivalence class. By exploiting this property, our algorithm reduces the search space to the space of equivalence classes, which it browses within a backtracking framework, hence emerging as an efficient yet relatively simple-to-implement or generalise solution method. We empirically evaluate our algorithm against the state-of-the-art methods and show that it clearly wins the competition on the whole range of our test problems and significantly extends the domain of practically solvable instances of the WSP

Search methods for tile sets in patterned DNA self-assembly

Peer reviewe

An investigation of distributed computing for combinatorial testing

Combinatorial test generation, also calledt-way testing, is the process ofgenerating sets of input parameters for a system under test, by consideringinteractions between values of multiple parameters. In order to decrease totaltesting time, there is an interest in techniques that generate smaller test suites.In our previous work, we used graph techniques to produce high-quality testsuites. However, these techniques require a lot of computing power andmemory, which is why this paper investigates distributed computing fort-waytesting. We first introduce our distributed graph colouring method, with newalgorithms for building the graph and for colouring it. Second, we present ourdistributed hypergraph vertex covering method and a new heuristic. Third, weshow how to build a distributed IPOG algorithm by leveraging either graphcolouring or hypergraph vertex covering as vertical growth algorithms.Finally, we test these new methods on a computer cluster and compare themto existingt-way testing tools

Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints

The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems.  In this paper, we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other.  Specifically, we consider the workflow satisfiability problem (WSP) which asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment.  It was shown by Cohen et al. (JAIR 2014) that WSP restricted to the class of user-independent constraints (UI), covering many practical cases, admits FPT algorithms, i.e. can be solved in time exponential only in the number of steps k and polynomial in the number of users n.  Since usually k << n in WSP, such FPT algorithms are of great practical interest. We present a new interpretation of the FPT nature of the WSP with UI constraints giving a decomposition of the problem into two levels.  Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm and also has only polynomial-space complexity.  We also introduce new pseudo-Boolean (PB) and Constraint Satisfaction (CSP) formulations of the WSP with UI constraints which efficiently exploit this new decomposition of the problem and raise the novel issue of how to use general-purpose solvers to tackle FPT problems in a fashion that meets FPT efficiency expectations.  In our computational study, we investigate, for the first time, the phase transition (PT) properties of the WSP, under a model for generation of random instances.  We show how PT studies can be extended, in a novel fashion, to support empirical evaluation of scaling of FPT algorithms

The multiple pheromone Ant clustering algorithm

Ant Colony Optimisation algorithms mimic the way ants use pheromones for marking paths to important locations. Pheromone traces are followed and reinforced by other ants, but also evaporate over time. As a consequence, optimal paths attract more pheromone, whilst the less useful paths fade away. In the Multiple Pheromone Ant Clustering Algorithm (MPACA), ants detect features of objects represented as nodes within graph space. Each node has one or more ants assigned to each feature. Ants attempt to locate nodes with matching feature values, depositing pheromone traces on the way. This use of multiple pheromone values is a key innovation. Ants record other ant encounters, keeping a record of the features and colony membership of ants. The recorded values determine when ants should combine their features to look for conjunctions and whether they should merge into colonies. This ability to detect and deposit pheromone representative of feature combinations, and the resulting colony formation, renders the algorithm a powerful clustering tool. The MPACA operates as follows: (i) initially each node has ants assigned to each feature; (ii) ants roam the graph space searching for nodes with matching features; (iii) when departing matching nodes, ants deposit pheromones to inform other ants that the path goes to a node with the associated feature values; (iv) ant feature encounters are counted each time an ant arrives at a node; (v) if the feature encounters exceed a threshold value, feature combination occurs; (vi) a similar mechanism is used for colony merging. The model varies from traditional ACO in that: (i) a modified pheromone-driven movement mechanism is used; (ii) ants learn feature combinations and deposit multiple pheromone scents accordingly; (iii) ants merge into colonies, the basis of cluster formation. The MPACA is evaluated over synthetic and real-world datasets and its performance compares favourably with alternative approaches

Examination scheduling using the ant system.

This work is concerned with heuristic approaches to examination timetabling. It is demonstrated that a relatively new evolutionary method, the Ant System, can be the basis of a successful two-phase solution method. The first phase exploits ant feedback in order both to produce large volumes of feasible timetables and to optimise secondary objectives. The second phase acts as a repair facility where solution quality is improved further while maintaining feasibility. This is accomplished without increasing computational effort to unrealistic levels. The work builds on an existing implementation for the graph colouring problem, the natural model for examination scheduling. It is demonstrated that by adjusting the graph model to allow the accommodation of several side constraints as well incorporating enhancement techniques within the algorithm itself, the Ant System algorithm becomes very effective at producing feasible timetables. The enhancements include a diversification function, new reward functions and trail replenishment tactics. It is observed that the achievement of second-order objectives can be enhanced through a variety of means. A modified elitist strategy (ERF) significantly improves the performance of the Ant System due to the extra emphasis on second-order feedback. It is also shown that through the incorporation of the ERF, trail limits and, in particular, 19th century evolutionary theory the area of the solution space explored by the ants during the infancy of the search can be reduced. In addition, a good level of exploration is maintained as the search matures. This balance between exploration and exploitation is the main determinant of solution quality. The use of a repair facility, as is common practice with evolutionary algorithms, encourages fitter solutions. The interaction between Lamarckian evolution and searching in an extended neighbourhood through the graph theoretic concept of Kempe chains leads to better overall solutions