Multi-threading a state-of-the-art maximum clique algorithm

We present a threaded parallel adaptation of a state-of-the-art maximum clique algorithm for dense, computationally challenging graphs. We show that near-linear speedups are achievable in practice and that superlinear speedups are common. We include results for several previously unsolved benchmark problems

Triangle packing with constraint programming

In vertex disjoint triangle packing we are given a simple undirected graph G and we have to select the maximum number of triangles such that each triangle is composed of three adjacent vertices and each pair of triangles selected has no vertex in common. The problem is NP-hard and APX-complete. We present three constraint models and apply them to the optimisation and decision problem (attempting to pack n/3 triangles in a graph with n vertices). In the decision problem we observe a phase transition from satisfiability to unsatisfiability, with a complexity peak at the point where 50% of instances are satisfiable, and this is expected. We characterise this phase transition theoretically with respect to constrainedness. However, when we apply a mixed integer programming model to the decision problem the complexity peak disappears

Oral transmucosal fentanyl

None availabl

Breaking Symmetries in Graph Representation

There are many complex combinatorial problems which involve searching for an undirected graph satisfying a certain property. These problems are often highly challenging because of the large number of isomorphic representations of a possible solution. In this paper we introduce novel, effective and compact, symmetry breaking constraints for undirected graph search. While incomplete, these prove highly beneficial in pruning the search for a graph. We illustrate the application of symmetry breaking in graph representation to resolve several open instances in extremal graph theory

A Parallel Branch and Bound Algorithm for the Maximum Labelled Clique Problem

The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new branch-and-bound algorithm for the problem, and explain how it may be parallelised. We evaluate an implementation on a set of benchmark instances, and show that it is consistently faster than previously published results, sometimes by four or five orders of magnitude.Comment: Author-final version. Accepted to Optimization Letter

Tunable entanglement distillation of spatially correlated down-converted photons

We report on a new technique for entanglement distillation of the bipartite continuous variable state of spatially correlated photons generated in the spontaneous parametric down-conversion process (SPDC), where tunable non-Gaussian operations are implemented and the post-processed entanglement is certified in real-time using a single-photon sensitive electron multiplying CCD (EMCCD) camera. The local operations are performed using non-Gaussian filters modulated into a programmable spatial light modulator and, by using the EMCCD camera for actively recording the probability distributions of the twin-photons, one has fine control of the Schmidt number of the distilled state. We show that even simple non-Gaussian filters can be finely tuned to a ~67% net gain of the initial entanglement generated in the SPDC process.Comment: 12 pages, 6 figure

An outside-inside view of exclusive practice within an inclusive mainstream school

This article is a reflection on a sabbatical experience in a mainstream school where an inclusive ethos underpinned the curriculum and environmental approaches for all children. The period as Acting Head teacher raised some challenges for me in reconciling inclusion for all children and the exclusive nature of some professional and physical spaces available to the community of adults working in the school. It has highlighted some development opportunities for the senior management of the school and its governing body

Transfer of academic staff learning in a research-intensive university

In both Australia and abroad, there is an increasing pressure towards professionalisation of university teaching, with the expectation that academic development courses, such as the Graduate Certificate in Education Studies (higher education), lead to better teaching and learning practices. However, the knowledge, skills and/or attitudes that educators intend students to learn may not transfer successfully back to the workplace. This may occur for a variety of reasons, including individual characteristics of the learner (e.g. ability, motivation), and situational characteristics (e.g. the climate for transfer, including adequacy of resources and peer/manager support). The present study investigates the impact of these factors on teaching staff in a research-intensive university. Two in-depth case studies, followed by thematic analysis of 15 Graduate Certificate alumni interviews regarding post-course experiences, revealed that qualities of the work environment played significant roles in interviewees’ postcourse attitudes, intentions and activities related to the transfer of learning. Implications for encouraging transfer under similar circumstances are discussed.postprin

On the reformulation of vehicle routing problems and scheduling problems

We can reformulate a vehicle routing problem (VRP) as an open shop scheduling problem (SSP) by representing visits as activities, vehicles as resources on the factory floor, and travel as set up costs between activities. In this paper we present two reformulations: from VRP to open shop, and the inverse, from SSP to VRP. Not surprisingly, VRP technology performs poorly on reformulated SSP's, as does scheduling technology on reformulated VRP's. We present a pre-processing transformation that "compresses" the VRP, transforming an element of travel into the duration of the visits. The compressed VRP's are then reformulated as scheduling problem, to determine if it is primarily distance in the VRP that causes scheduling technology to degrade on the reformulated problem. This is a step towards understanding the features of a problem that make it more amenable to one technology rather than another