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

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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

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

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

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

Anoxic nitrification in marine sediments

Nitrate peaks are found in pore-water profiles in marine sediments at depths considerably below the conventional zone of oxic nitrification. These have been interpreted to represent nonsteady- state effects produced by the activity of nitrifying bacteria, and suggest that nitrification occurs throughout the anoxic sediment region. In this study, ΣNO3 peaks and molecular analysis of DNA and RNA extracted from anoxic sediments of Loch Duich, an organic-rich marine fjord, are consistent with nitrification occurring in the anoxic zone. Analysis of ammonia oxidiser 16S rRNA gene fragments amplified from sediment DNA indicated the abundance of autotrophic ammonia-oxidising bacteria throughout the sediment depth sampled (40 cm), while RT-PCR analysis indicated their potential activity throughout this region. A large non-steady-state pore-water ΣNO3 peak at ~21 cm correlated with discontinuities in this ammonia-oxidiser community. In addition, a subsurface nitrate peak at ~8 cm below the oxygen penetration depth, correlated with the depth of a peak in nitrification rate, assessed by transformation of 15N-labelled ammonia. The source of the oxidant required to support nitrification within the anoxic region is uncertain. It is suggested that rapid recycling of N is occurring, based on a coupled reaction involving Mn oxides (or possibly highly labile Fe oxides) buried during small-scale slumping events. However, to fully investigate this coupling, advances in the capability of high-resolution pore-water techniques are required

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

Graph transformations for the vehicle routing and job shop scheduling problems

The vehicle routing problem (VRP) and job shop scheduling problem (JSP) are two common combinatorial problems that can be naturally represented as graphs. A core component of solving each problem can be modeled as finding a minimum cost Hamiltonian path in a complete weighted graph. The graphs extracted from VRPs and JSPs have different characteristics however, notably in the ratio of edge weight to node weight. Our long term research question is to determine the extent to which such graph characteristics impact the performance of algorithms commonly applied to VRPs and JSPs. As a preliminary step, in this paper we investigate five transformations for complete weighted graphs that preserve the cost of Hamiltonian paths. These transformations are based on increasing node weights while reducing edge weights or the inverse. We demonstrate how the transformations affect the ratio of edge to node weight and how they change the relative weights of edges at a node. Finally, we conjecture how the different transformations will impact the performance of existing VRP and JSP solving techniques