Augmenting graphs to minimize the diameter

We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure

Rematerialising Heritage

The Rocks is one of Sydney's premier tourist locations; its identity largely founded on the perception of it as a historically significant site. This perception is steeped in complex notions of the `authentic tourist experience offered at The Rocks, which arguably originates from the retention of some of the early streets and architectures of the area. However, implicit in the act of retention is also the act of deletion. Throughout the area of The Rocks, gaps exist. These are the spaces where buildings, houses, outhouses, lanes and indeed whole streets have been eradicated to make way for urban progress or to redefine areas of the city according to political or economic aims. Heritage here is constructed, not only from that which is retained and preserved but also from that which is deleted and destroyed. This paper seeks to examine the fate of one particular street in the Rocks Princes Street that was eradicated in 1927 to make way for the Sydney Harbour Bridge. The physical demolition of the street and subsequent erasure of any material sign of it has effectively allowed the street to disappear. The predominant historical narrative that results reveals the extent to which current notions of the past are fundamentally understood through the existence of the material artefact. Yet this paper argues that definitions of the past can be drawn, not only from the material or architectural object that operates as historical proof but also from the social, performative and touristic acts that might be undertaken around the object, the architecture or even its representation

Speeding up shortest path algorithms

Given an arbitrary, non-negatively weighted, directed graph $G=(V,E)$ we present an algorithm that computes all pairs shortest paths in time $\mathcal{O}(m^* n + m \lg n + nT_\psi(m^*, n))$, where $m^*$ is the number of different edges contained in shortest paths and $T_\psi(m^*, n)$ is a running time of an algorithm to solve a single-source shortest path problem (SSSP). This is a substantial improvement over a trivial $n$ times application of $\psi$ that runs in $\mathcal{O}(nT_\psi(m,n))$. In our algorithm we use $\psi$ as a black box and hence any improvement on $\psi$ results also in improvement of our algorithm. Furthermore, a combination of our method, Johnson's reweighting technique and topological sorting results in an $\mathcal{O}(m^*n + m \lg n)$ all-pairs shortest path algorithm for arbitrarily-weighted directed acyclic graphs. In addition, we also point out a connection between the complexity of a certain sorting problem defined on shortest paths and SSSP.Comment: 10 page

Lower bounds in the quantum cell probe model

We introduce a new model for studying quantum data structure problems --- the "quantum cell probe model". We prove a lower bound for the static predecessor problem in the 'address-only' version of this model where, essentially, we allow quantum parallelism only over the 'address lines' of the queries. This model subsumes the classical cell probe model, and many quantum query algorithms like Grover's algorithm fall into this framework. We prove our lower bound by obtaining a round elimination lemma for quantum communication complexity. A similar lemma was proved by Miltersen, Nisan, Safra and Wigderson for classical communication complexity, but their proof does not generalise to the quantum setting. We also study the static membership problem in the quantum cell probe model. Generalising a result of Yao, we show that if the storage scheme is 'implicit', that is it can only store members of the subset and 'pointers', then any quantum query scheme must make \Omega(\log n) probes. We also consider the one-round quantum communication complexity of set membership and show tight bounds

Caregiving, Metabolic Syndrome Indicators, and 1-year Decline in Walking Speed: Results of Caregiver-SOF

BACKGROUND Chronic stress may lead to health decline through metabolic syndrome. Thus, persons in stressful caregiving situations who also have more indicators of metabolic syndrome may experience more decline than other caregivers or noncaregivers. METHODS The sample included 921 women (338 caregivers and 583 noncaregivers) from the Caregiver-Study of Osteoporotic Fractures study. Participants had home-based baseline and 1-year follow-up interviews between 1999 and 2003. At baseline, caregivers were categorized as long term (³4 years) versus short term (<4 years), and caring for someone with Alzheimer's disease/dementia or not. A metabolic risk composite score was the sum of four indicators: body mass index ³30, and diagnosis or using medications for hypertension, diabetes, or high cholesterol. Walking speed (m/second) was measured at both interviews. RESULTS Walking speed declined for the total sample (adjusted mean = −0.005 m/second, ±0.16) over an average of 1.04 years (±0.16). Overall, caregiving was not associated with decline. Increasing metabolic risk score was associated with greater decline for the total sample and long-term and dementia caregivers, but not other caregivers or noncaregivers. Metabolic risk score modified the adjusted associations between years of caregiving and dementia caregiving with walking speed decline (p values for interaction terms were 0.039 and 0.057, respectively). The biggest declines were in long-term caregivers and dementia caregivers who also had 3–4 metabolic indicators (−0.10 m/second and −0.155 m/second, respectively). CONCLUSIONS Walking speed declined the most among older women who had both stressful caregiving situations and more metabolic syndrome indicators, suggesting these caregiver subgroups may have increased risk of health decline.AG18037, AG05407, AR35582, AG05394, AR35584, and AR3558

On dualization in products of forests, in

Abstract. Let P = P1 ×...×Pn be the product of n partially ordered sets, each with an acyclic precedence graph in which either the in-degree or the out-degree of each element is bounded. Given a subset A⊆P,it is shown that the set of maximal independent elements of A in P can be incrementally generated in quasi-polynomial time. We discuss some applications in data mining related to this dualization problem

Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

Effect of Diabetes and Glycemic Control on&nbsp;Ischemic Stroke Risk in AF Patients ATRIA Study

BackgroundDiagnosed diabetes mellitus (DM) is a consistently documented risk factor for ischemic stroke in patients&nbsp;with atrial fibrillation (AF).ObjectivesThe purpose of this study was to assess the association between duration of diabetes and elevated hemoglobin&nbsp;A1c (HbA1c) with risk of stroke among diabetic patients with AF.MethodsWe assessed this association in the ATRIA (Anticoagulation and Risk Factors in Atrial Fibrillation) California community-based cohort of AF patients (study years 1996 to 2003) where all events were clinician adjudicated. We used Cox proportional hazards regression to estimate the rate of ischemic stroke in diabetic patients according to time-varying measures of estimated duration of diabetes (≥3 years compared with&nbsp;&lt;3 years) and HbA1c values (≥9.0% and 7.0% to 8.9% compared with&nbsp;&lt;7.0%), focusing on periods where patients were not anticoagulated.ResultsThere were 2,101 diabetic patients included in the duration analysis: 40% with duration&nbsp;&lt;3 years and 60%&nbsp;with duration&nbsp;≥3 years at baseline. Among 1,933 diabetic patients included in the HbA1c analysis, 46% had HbA1c&nbsp;&lt;7.0%, 36% between 7.0% and 8.9%, and 19%&nbsp;≥9.0% at baseline. Duration of diabetes&nbsp;≥3 years was associated with an increased rate of ischemic stroke compared with duration&nbsp;&lt;3 years (adjusted hazard ratio [HR]: 1.74, 95% confidence interval [CI]: 1.10 to 2.76). The increased stroke rate was observed in older (age&nbsp;≥75 years) and younger (age&nbsp;&lt;75 years) individuals. Neither poor glycemic control (HbA1c&nbsp;≥9.0%, adjusted HR: 1.04, 95% CI: 0.57 to 1.92) nor moderately increased HbA1c (7.0% to 8.9%, adjusted HR: 1.21, 95% CI: 0.77 to 1.91) were significantly associated with an increased rate of ischemic stroke compared with patients who had HbA1c&nbsp;&lt;7.0%.ConclusionsDuration of diabetes is a more important predictor of ischemic stroke than glycemic control in patients who have diabetes and AF

Separating Hierarchical and General Hub Labelings

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201

Bridging the gap: an exploration of the use and impact of positive action in the UK

Despite laws in Britain permitting limited positive action initiatives to combat disadvantage faced by minority groups in employment since the mid-1970s, the subject has notoriously been a neglected and highly controversial area in the UK. Notwithstanding the potential provided by sections 158 and 159 of the Equality Act 2010, it still appears that organisations prefer to steer clear of this opportunity to address disadvantage suffered by protected groups. Whilst there is a body of work considering the theoretical importance of positive action in the UK, there is a lack of empirical exploration of the practical implications of these provisions. This paper will provide a brief overview of the theoretical context and current positive action legislative provisions within the UK. In light of this context, the early findings of a small-scale qualitative study carried out by the authors will be discussed looking at the experiences of a purposive sample of public and private employers in relation to the positive action provisions of the Equality Act 2010. Early research findings suggest that whilst there was a clear willingness and openness by employers to use of outreach measures in order to redress disadvantage, there was evident wariness regarding a move towards preferential treatment as expounded by section 159. Whilst respondents appeared to appreciate the business case for and utility of the positive action measures under section 158, there was far less enthusiasm for more direct preferential treatment, with many respondents raising serious concerns regarding this. These concerns often reflected a highly sensitive risk-based approach towards any action that could expose their organisation to the possibility of “reverse discrimination”