Randomized Algorithms for the Loop Cutset Problem

We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding a loop cutset outputs a minimum loop cutset after O(c 6^k kn) steps with probability at least 1 - (1 - 1/(6^k))^c6^k, where c > 1 is a constant specified by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often finds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known

Fast Structuring of Radio Networks for Multi-Message Communications

We introduce collision free layerings as a powerful way to structure radio networks. These layerings can replace hard-to-compute BFS-trees in many contexts while having an efficient randomized distributed construction. We demonstrate their versatility by using them to provide near optimal distributed algorithms for several multi-message communication primitives. Designing efficient communication primitives for radio networks has a rich history that began 25 years ago when Bar-Yehuda et al. introduced fast randomized algorithms for broadcasting and for constructing BFS-trees. Their BFS-tree construction time was $O(D \log^2 n)$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. Since then, the complexity of a broadcast has been resolved to be $T_{BC} = \Theta(D \log \frac{n}{D} + \log^2 n)$ rounds. On the other hand, BFS-trees have been used as a crucial building block for many communication primitives and their construction time remained a bottleneck for these primitives. We introduce collision free layerings that can be used in place of BFS-trees and we give a randomized construction of these layerings that runs in nearly broadcast time, that is, w.h.p. in $T_{Lay} = O(D \log \frac{n}{D} + \log^{2+\epsilon} n)$ rounds for any constant $\epsilon>0$. We then use these layerings to obtain: (1) A randomized algorithm for gathering $k$ messages running w.h.p. in $O(T_{Lay} + k)$ rounds. (2) A randomized $k$-message broadcast algorithm running w.h.p. in $O(T_{Lay} + k \log n)$ rounds. These algorithms are optimal up to the small difference in the additive poly-logarithmic term between $T_{BC}$ and $T_{Lay}$. Moreover, they imply the first optimal $O(n \log n)$ round randomized gossip algorithm

Connections between two cycles — a new design of dense processor interconnection networks

AbstractIn this paper we attempt to maximize the order of graphs of given degree Δ and diameter D. These graphs, which are known as (Δ, D) graphs, are used as dense interconnection networks, i.e., processors with relatively few links are connected with relatively short paths. The method described in this paper uses periodic connections between two cycles of the same length. The results obtained give a significant improvement of the known lower bounds in many cases. Large bipartite graphs with a given degree and diameter were also obtained by our method. Again, the improvement of the lower bounds is significant

Learning from screen media in early childhood: a double-edged sword

The present study aims to examine the long-term process of learning from screen in early childhood in the child’s familial environment. Specificall , it focuses on the process of screen-aided acquisition of a second language by a young girl (here called Dana) who was 12 months old at the beginning of the study and three years old towards its end. The family was selected for in-depth analysis because of the great emphasis that Dana’s mother placed on use of touchscreen media to support her daughter’s learning of English. First and foremost, the research findings demonstrate the limitations of this use, especially when it is not accompanied by appropriate parental mediation. The study shows that use of a smartphone for learning purposes without the mother’s instructive mediation was barely able to advance Dana’s English acquisition that was limited to phonetic elements only. Moreover, the findings reveal that with her mother’s encouragement, Dana acquired highly problematic smartphone use habits that could be harmful to her health and development. Hence, the research findings call for increasing media literacy among parents of infants and toddlers who need to know how to support the development of appropriate media habits among their young children.info:eu-repo/semantics/publishedVersio

Digital Parenting: Media Uses in Parenting Routines during the First Two Years of Life

According to the American Academy of Pediatrics, children younger than 18 months of age should have no access to screen media, while children aged 18 to 24 months may be allowed occasional viewing of high-quality children’s programs together with their parents. Despite these stringent recommendations, however, television and digital devices manifest significant presence in the everyday lives of very young children, even during infancy. Therefore, major empirical efforts were exerted to reveal various predictors of young children’s screen time and suggest effective means for its reduction. Along these lines, the present study examined parental media practices applied during infancy and early toddlerhood and how these practices contribute to children’s excessive media exposure during the first two years of their life. It was based on a longitudinal study which followed ten families with children from the age of three months until they reached two years, and included a series of observations at the families’ homes and in-depth interviews with parents. The findings reveal that parents extensively exposed their children to screen devices, which played a significant role in the daily parenting routines. All parents used screens as a “background,” a “babysitter”, a “pacifier” and a “childcare toolkit”, regardless of their own attitudes towards media effects on their young children. Consequently, it is suggested to increase parental awareness towards their instrumental use of media as part of their parenting routine, which may impart unhealthy media habits and affect their children’s long-term development

Distributed Approximation of Maximum Independent Set and Maximum Matching

We present a simple distributed $\Delta$-approximation algorithm for maximum weight independent set (MaxIS) in the $\mathsf{CONGEST}$ model which completes in $O(\texttt{MIS}(G)\cdot \log W)$ rounds, where $\Delta$ is the maximum degree, $\texttt{MIS}(G)$ is the number of rounds needed to compute a maximal independent set (MIS) on $G$, and $W$ is the maximum weight of a node. %Whether our algorithm is randomized or deterministic depends on the \texttt{MIS} algorithm used as a black-box. Plugging in the best known algorithm for MIS gives a randomized solution in $O(\log n \log W)$ rounds, where $n$ is the number of nodes. We also present a deterministic $O(\Delta +\log^* n)$-round algorithm based on coloring. We then show how to use our MaxIS approximation algorithms to compute a $2$-approximation for maximum weight matching without incurring any additional round penalty in the $\mathsf{CONGEST}$ model. We use a known reduction for simulating algorithms on the line graph while incurring congestion, but we show our algorithm is part of a broad family of \emph{local aggregation algorithms} for which we describe a mechanism that allows the simulation to run in the $\mathsf{CONGEST}$ model without an additional overhead. Next, we show that for maximum weight matching, relaxing the approximation factor to ($2+\varepsilon$) allows us to devise a distributed algorithm requiring $O(\frac{\log \Delta}{\log\log\Delta})$ rounds for any constant $\varepsilon>0$. For the unweighted case, we can even obtain a $(1+\varepsilon)$-approximation in this number of rounds. These algorithms are the first to achieve the provably optimal round complexity with respect to dependency on $\Delta$

Hitting Diamonds and Growing Cacti

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is \Theta(\log n), where n denotes the number of vertices in the graph.Comment: v2: several minor changes