Approximability of Connected Factors

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard - finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected $d$-factor. We give a 3-approximation for all $d$ and improve this to an (r+1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r+1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.Comment: To appear in the proceedings of WAOA 201

Study of distributed coordination function (DCF) and enhanced dcf (EDCF) in IEEE 802.11 MAC protocols for multimedia applications

IEEE 802.11e Medium Access Control (MAC) is an enhancement to the legacy IEEE 802.11 standard’s Wireless Local Area Network (WLAN) ideally to support Quality-ofService (QOS). The 802.11e MAC is both centrally-controlled and contention-based channel accesses based. This project covers evaluation of the contention-based channel access mechanism, called Enhanced Distributed Coordination Function (EDCF), in comparison with the 802.11 legacy MAC, Distributed Coordination Function. Three different types of multimedia traffic are considered namely, voice, video and data. The evaluation was performed using ns-2 simulator (version 2.34) on Linux Ubuntu. The metrics used in the evaluation are throughput, delay, jitters and packet loss. The graphs from the metrics benchmarked the performance of EDCF and DCF evaluation. Through this simulation study, EDCF conclusively provides differentiated channel access for various multimedia traffic types. Simulation results proved that comparatively EDCF performs better performance than legacy DCF

Experiences of COVID-19 among Chinese-speaking lesbian, gay and bisexual people in Hong Kong: an inductive thematic analysis of survey response data

As social inequalities during the COVID-19 pandemic have been recognised, emerging research showed that lesbian, gay and bisexual (LGB) people may be additionally affected during the pandemic. This paper adds to the understanding of the experiences of LGB people during the pandemic with a focus on Hong Kong, where issues of space significantly influence LGB people’s lives in this city with high population density. As part of a larger community study of LGB lives in Hong Kong, COVID-19-related impact on 434 Chinese-speaking LGB people was explored. Data collection was conducted from 20 May to 30 June 2020. Inductive thematic analysis of the open-text response survey data found that the LGB participants described both negative and positive impacts brought by COVID-19. Such impacts could be dimensionalised into those related to personal space and privacy, romantic and sexual space, and community space. It was also found that the experiences of COVID-19 among LGB people in Hong Kong were intersectional, along the lines of living arrangement and relationship status. Such findings make unique contributions to the emerging literature. First, there needs to be a more nuanced understanding of sexual minority individuals’ experiences during COVID-19 across cultural contexts. Second, COVID-19 was described as having brought positive impact in addition to its widely known negative impact

An exploratory study of factors associated with difficulties in accessing HIV services during the COVID-19 pandemic among Chinese gay and bisexual men in Hong Kong

Background: The coronavirus disease 2019 (COVID-19) pandemic has resulted in the disruption of provision of human immunodeficiency virus (HIV) services. This study examined the factors associated with difficulties in accessing HIV services during the COVID-19 pandemic. Methods: An online survey of 236 Chinese-speaking gay and bisexual men in Hong Kong conducted in 2020. Results: Among those who expressed a need to access HIV services during the COVID-19 pandemic, 22.9%, 33.9% and 43.2% indicated moderate-to-high, mild and no difficulties in accessing these services, respectively. Difficulties in accessing HIV services were positively related to concerns about potential COVID-19 infection, experience of actual impact on health because of COVID-19, disruption in work/studies, and reduced connection to the LGBT+ community during the pandemic. It was also found that difficulties in accessing HIV services were positively associated with frequency of having sex with casual partners, but were not significantly associated with frequency of having sex with regular partners. Conclusions: This study provides novel empirical evidence for understanding difficulties in accessing HIV services during the COVID-19 pandemic. It found that disruption in work/studies and frequency of having sex with casual partners were associated with difficulties in accessing HIV services

Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time variable.Comment: 14 pages, to appea

Bounded-Angle Spanning Tree: Modeling Networks with Angular Constraints

We introduce a new structure for a set of points in the plane and an angle $\alpha$, which is similar in flavor to a bounded-degree MST. We name this structure $\alpha$-MST. Let $P$ be a set of points in the plane and let $0 < \alpha \le 2\pi$ be an angle. An $\alpha$-ST of $P$ is a spanning tree of the complete Euclidean graph induced by $P$, with the additional property that for each point $p \in P$, the smallest angle around $p$ containing all the edges adjacent to $p$ is at most $\alpha$. An $\alpha$-MST of $P$ is then an $\alpha$-ST of $P$ of minimum weight. For $\alpha < \pi/3$, an $\alpha$-ST does not always exist, and, for $\alpha \ge \pi/3$, it always exists. In this paper, we study the problem of computing an $\alpha$-MST for several common values of $\alpha$. Motivated by wireless networks, we formulate the problem in terms of directional antennas. With each point $p \in P$, we associate a wedge $W_p$ of angle $\alpha$ and apex $p$. The goal is to assign an orientation and a radius $r_p$ to each wedge $W_p$, such that the resulting graph is connected and its MST is an $\alpha$-MST. (We draw an edge between $p$ and $q$ if $p \in W_q$, $q \in W_p$, and $|pq| \le r_p, r_q$.) Unsurprisingly, the problem of computing an $\alpha$-MST is NP-hard, at least for $\alpha=\pi$ and $\alpha=2\pi/3$. We present constant-factor approximation algorithms for $\alpha = \pi/2, 2\pi/3, \pi$. One of our major results is a surprising theorem for $\alpha = 2\pi/3$, which, besides being interesting from a geometric point of view, has important applications. For example, the theorem guarantees that given any set $P$ of $3n$ points in the plane and any partitioning of the points into $n$ triplets, one can orient the wedges of each triplet {\em independently}, such that the graph induced by $P$ is connected. We apply the theorem to the {\em antenna conversion} problem

Theory-based behavioral change interventions to improve periodontal health

Periodontal disease is a significant global health burden affecting half of the world's population. Given that plaque and inflammation control are essential to the attainment of periodontal health, recent trends in preventive dentistry have focused on the use of behavioral models to understand patient psychology and promote self-care and treatment compliance. In addition to their uses in classifying, explaining and predicting oral hygiene practices, behavioral models have been adopted in the design of oral hygiene interventions from individual to population levels. Despite the growing focus on behavioral modification in dentistry, the currently available evidence in the field of periodontology is scarce, and interventions have primarily measured changes in patient beliefs or performance in oral hygiene behaviors. Few studies have measured their impact on clinical outcomes, such as plaque levels, gingival bleeding and periodontal pocket reduction, which serve as indicators of the patient's disease status and quality of oral self-care. The present narrative review aims to summarize selected literature on the use of behavioral models to improve periodontal outcomes. A search was performed on existing behavioral models used to guide dental interventions to identify their use in interventions measuring periodontal parameters. The main models were identified and subsequently grouped by their underlying theoretical area of focus: patient beliefs (health belief model and cognitive behavioral principles); stages of readiness to change (precaution adoption process model and transtheoretical model); planning behavioral change (health action process approach model, theory of planned behavior and client self-care commitment model); and self-monitoring (self-regulation theory). Key constructs of each model and the findings of associated interventions were described. The COM-B model, a newer behavioral change system that has been increasingly used to guide interventions and policy changes, is discussed with reference to its use in oral health settings. Within the limitations of the available evidence, interventions addressing patient beliefs, motivation, intention and self-regulation could lead to improved outcomes in periodontal health. Direct comparisons between interventions could not be made due to differences in protocol design, research populations and follow-up periods. The conclusions of this review assist clinicians with implementing psychological interventions for oral hygiene promotion and highlight the need for additional studies on the clinical effects of behavioral model-based interventions