36 research outputs found

    Stronger ILPs for the Graph Genus Problem

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    The minimum genus of a graph is an important question in graph theory and a key ingredient in several graph algorithms. However, its computation is NP-hard and turns out to be hard even in practice. Only recently, the first non-trivial approach - based on SAT and ILP (integer linear programming) models - has been presented, but it is unable to successfully tackle graphs of genus larger than 1 in practice. Herein, we show how to improve the ILP formulation. The crucial ingredients are two-fold. First, we show that instead of modeling rotation schemes explicitly, it suffices to optimize over partitions of the (bidirected) arc set A of the graph. Second, we exploit the cycle structure of the graph, explicitly mapping short closed walks on A to faces in the embedding. Besides the theoretical advantages of our models, we show their practical strength by a thorough experimental evaluation. Contrary to the previous approach, we are able to quickly solve many instances of genus > 1

    Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast

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    The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph H of a given graph G such that H has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear programming and Kuratowski\u27s famous planarity criterion. We build upon this approach and present new constraint classes - together with a lifting of the polyhedron - to obtain provably stronger LP-relaxations, and in turn faster algorithms in practice. The new constraints take Euler\u27s polyhedron formula as a starting point and combine it with considering cycles in G. This paper discusses both the theoretical as well as the practical sides of this strengthening

    Re-cognising RPL – A Deleuzian enquiry into policy and practice of Recognition of Prior Learning

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    This enquiry addresses a gap in the literature in relation to the conceptual development of Recognition of Prior Learning. Generally, research in RPL comprises large inventories and audits of practice as this enquiry shows. Few qualitative studies are available and there is a dearth of theoretical development in the field. This thesis explores perspectives of claimants and university managers/practitioners to explicate the issues at stake and explore the value of RPL in education. Using the practical philosophy of Gilles Deleuze and Felix Guattari (DG), the conceptualization of RPL is explored in policy and practice and their concepts are employed to reimagine RPL for learning, and as pedagogy, in adult university education. A hybrid method of grounded and rhizomatic theory informs the research approach. This involves searching the complex and diffuse territory of RPL to seek affirmative options for RPL theory and practice. Three case studies illustrate how different approaches to RPL offer different outcomes and were built on vague conceptualizations. In one setting, fifteen years of RPL claimant records is collated and analysed. Findings show that up to 70% of adult students in the case study had prior learning and gained exemptions. The data further indicates that RPL did not increase a student’s chances of completing a degree. This contradicts findings from international research. The research also challenges fears expressed by university managers that RPL poses a risk to academic standards, as claimants may not have foundational knowledge to succeed in university. The data indicates, however, that on the contrary, claimants have extensive prior learning; much of it accredited at levels 6 and 7 and are thus college ready. A model of learner directed RPL, used in another setting, is explored and theorized. This creative approach seamlessly integrates prior learning with new learning and thereby advances knowledge for the learner. The impact of the approach on the learner and learning is significant and offers new possibilities for RPL in education. It moves it on from the narrow purpose of reducing time in education and enhancing skills for employment. Accounts from participants in this enquiry show that they go to college to learn and they prize RPL most when it extends their knowledge – a dimension of RPL neglected in the literature. The thesis concludes with some affirmative options for re-cognising RPL in adult education

    Re-cognising RPL – A Deleuzian enquiry into policy and practice of Recognition of Prior Learning

    Get PDF
    This enquiry addresses a gap in the literature in relation to the conceptual development of Recognition of Prior Learning. Generally, research in RPL comprises large inventories and audits of practice as this enquiry shows. Few qualitative studies are available and there is a dearth of theoretical development in the field. This thesis explores perspectives of claimants and university managers/practitioners to explicate the issues at stake and explore the value of RPL in education. Using the practical philosophy of Gilles Deleuze and Felix Guattari (DG), the conceptualization of RPL is explored in policy and practice and their concepts are employed to reimagine RPL for learning, and as pedagogy, in adult university education. A hybrid method of grounded and rhizomatic theory informs the research approach. This involves searching the complex and diffuse territory of RPL to seek affirmative options for RPL theory and practice. Three case studies illustrate how different approaches to RPL offer different outcomes and were built on vague conceptualizations. In one setting, fifteen years of RPL claimant records is collated and analysed. Findings show that up to 70% of adult students in the case study had prior learning and gained exemptions. The data further indicates that RPL did not increase a student’s chances of completing a degree. This contradicts findings from international research. The research also challenges fears expressed by university managers that RPL poses a risk to academic standards, as claimants may not have foundational knowledge to succeed in university. The data indicates, however, that on the contrary, claimants have extensive prior learning; much of it accredited at levels 6 and 7 and are thus college ready. A model of learner directed RPL, used in another setting, is explored and theorized. This creative approach seamlessly integrates prior learning with new learning and thereby advances knowledge for the learner. The impact of the approach on the learner and learning is significant and offers new possibilities for RPL in education. It moves it on from the narrow purpose of reducing time in education and enhancing skills for employment. Accounts from participants in this enquiry show that they go to college to learn and they prize RPL most when it extends their knowledge – a dimension of RPL neglected in the literature. The thesis concludes with some affirmative options for re-cognising RPL in adult education

    F-actin and integrin like proteins in Phytophthora cinnamomi

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    Tip growth is the primary form of growth in hyphal organisms and some plant cells. Tip growth in hyphae is highly dependent on F-actin, which acts to regulate and support growth. One of the models suggested for tip growth, the amebae model of tip growth, suggests that F-actin may also be the primary source of protrusive force for tip growth in some conditions, and that proteins with a similar function to animal integrins would be present an involved in tip growth (Heath and Steinberg 1999). In this thesis we examine the role of F-actin in the growth of the oomycete Phytophthora cinnamomi and the effects on growth of the F-actin disrupting compound Latrunculin B. We demonstrate that F-actin plays a critical role in the tip growth of Phytophthora cinnamomi with it's disruption causing rapid cessation in directional growth, followed by significant subapical swelling. Further more we examine Phytophthora cinnamomi for the presence of an B4 integrin like protein that has been previously reported in the oomycete Achlya bisexualis (Chitcholtan & Garrill 2005) and show that the B4 integrin like protein is not present in Phytophthora cinnamomi. These experiments help further our understanding of tip growth in Phytophthora cinnamomi an economically important plant pathogen

    The Complexity of Distributed Approximation of Packing and Covering Integer Linear Programs

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    In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability 11/poly(n)1 - 1/poly(n). Specifically, we show how to compute an (ϵ,O(lognϵ))\left(\epsilon, O\left(\frac{\log n}{\epsilon}\right)\right) low-diameter decomposition in O(log3(1/ϵ)lognϵ)O\left(\frac{\log^3(1/\epsilon)\log n}{\epsilon}\right) round Further developing our techniques, we show new distributed algorithms for approximating general packing and covering integer linear programs in the LOCAL model. For packing problems, our algorithm finds an (1ϵ)(1-\epsilon)-approximate solution in O(log3(1/ϵ)lognϵ)O\left(\frac{\log^3 (1/\epsilon) \log n}{\epsilon}\right) rounds with probability 11/poly(n)1 - 1/poly(n). For covering problems, our algorithm finds an (1+ϵ)(1+\epsilon)-approximate solution in O((loglogn+log(1/ϵ))3lognϵ)O\left(\frac{\left(\log \log n + \log (1/\epsilon)\right)^3 \log n}{\epsilon}\right) rounds with probability 11/poly(n)1 - 1/poly(n). These results improve upon the previous O(log3nϵ)O\left(\frac{\log^3 n}{\epsilon}\right)-round algorithm by Ghaffari, Kuhn, and Maus [STOC 2017] which is based on network decompositions. Our algorithms are near-optimal for many fundamental combinatorial graph optimization problems in the LOCAL model, such as minimum vertex cover and minimum dominating set, as their (1±ϵ)(1\pm \epsilon)-approximate solutions require Ω(lognϵ)\Omega\left(\frac{\log n}{\epsilon}\right) rounds to compute.Comment: To appear in PODC 202

    CHARACTERISATION AND MOLECULAR TYPING OF CLINICAL AND ENVIRONMENTAL ISOLATES OF VIBRIO PARAHAEMOLYTICUS

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    Vibrio parahaemolyticus is a natural inhabitant of coastal waters worldwide and is the leading cause of seafood-borne gastroenteritis. This study reports on the use of several molecular characterisation methods to screen clinical and environmental isolates of V parahaemolyticus to assess whether such techniques can be used to distinguish pathogenic isolates reliably. In a total of 86 isolates mainly of V parahaemolyticus but also including V cholerae, V vulnificus and several other species, serotypes of the more virulent clonal group 03:K6 were identified, but otherwise there appeared no association with serotype and phenotype. The tdh and trh genes encoding haemolysins that are typically associated with virulent isolates were found in a significantly large number of isolates; however, poor concordance between haemolytic activity and the presence of the gene tdh was found. In an effort to establish more accurate relationships amongst clinical and environmental isolates of V parahaemolyticus, four molecular typing systems were employed; namely pulsed-field gel electrophoresis (PFGE), intergenic transcribed spacer (ITS) analysis, tDNA intergenic length polymorphisms (tDNA-ILPs) and randomly amplified polymorphic DNA (RAPD). Typing patterns and clustering analysis using these methods differentiated V parahaemolyticus from other marine species as well as at the subspecies level. PFGE with NotI was shown to be the most discriminative but suffered from not being universally applicable. Both ITS and tDNA-ILP methods were sufficiently discriminatory with discrimination indices (DI) of between 0.568 and 0.724, depending on the primers employed. The discriminatory ability of RAPD was also affected by the primers used (DI= 0.959 - 0.965) but closely matched that of PFGE (DI = 0.976). Additionally, both RAPD methods were able to distinguish putative markers for the pandemic clonal group. Typing systems appeared largely stable in duplicate and triplicate analyses with multiple primer pairs with some obvious variability in the reproduction of faint amplicons. All methods except PFGE were simple to execute but none of the methods could distinguish V parahaemolyticus into obvious lineages based on the clinical or environmental source. With the recent implication of a type Ill secretion system {TTSS) involved in the pathogenicity of V parahaemolyticus, a multiplex PCR system using PCR primers that spanned both TTSSl and TTSS2 regions was developed. Dot-blot analysis confirmed TTSS2 genes in at least 30% of environmental isolates. Nucleotide sequence analysis revealed l00% sequence homology in three loci of TTSS2 putative structural genes. In comparison, a total of 34 single nucleotide polymorphisms (SNP) were identified in three TTSS1 regions. In two of the regions, the SNPs were synonymous, whereas a non-synonymous substitution in the structural gene vcrDI resulted in valine replacement with isoleucine. In addition, nucleotide deletions in TTSS1 with resultant frameshift mutations were identified. The finding that significant numbers of environmental isolates also possess TTSS2 genes is contrary to currently held opinion that TTSS2 is only present in clinical isolates. It is hypothesed that the high incidences of V parahaemolyticus infections may be related to active TTSS2 genes, whereas a high degree of polymorphisms in TTSS1 suggest it may be inactive.The Centre for Environment, Fisheries and Aquaculture Science Weymouth Laboratories, Dorset, United Kingdo

    Grundy Distinguishes Treewidth from Pathwidth

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    Structural graph parameters, such as treewidth, pathwidth, and clique-width, are a central topic of study in parameterized complexity. A main aim of research in this area is to understand the "price of generality" of these widths: as we transition from more restrictive to more general notions, which are the problems that see their complexity status deteriorate from fixed-parameter tractable to intractable? This type of question is by now very well-studied, but, somewhat strikingly, the algorithmic frontier between the two (arguably) most central width notions, treewidth and pathwidth, is still not understood: currently, no natural graph problem is known to be W-hard for one but FPT for the other. Indeed, a surprising development of the last few years has been the observation that for many of the most paradigmatic problems, their complexities for the two parameters actually coincide exactly, despite the fact that treewidth is a much more general parameter. It would thus appear that the extra generality of treewidth over pathwidth often comes "for free". Our main contribution in this paper is to uncover the first natural example where this generality comes with a high price. We consider Grundy Coloring, a variation of coloring where one seeks to calculate the worst possible coloring that could be assigned to a graph by a greedy First-Fit algorithm. We show that this well-studied problem is FPT parameterized by pathwidth; however, it becomes significantly harder (W[1]-hard) when parameterized by treewidth. Furthermore, we show that Grundy Coloring makes a second complexity jump for more general widths, as it becomes para-NP-hard for clique-width. Hence, Grundy Coloring nicely captures the complexity trade-offs between the three most well-studied parameters. Completing the picture, we show that Grundy Coloring is FPT parameterized by modular-width.Comment: To be published in proceedings of ESA 202
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