Directed Acyclic Graphs (DAGs), which offer systematic representations of causal relationships, have become an established framework for the analysis of causal inference in epidemiology; often being used to determine covariate adjustment sets for minimizing confounding bias. DAGitty is a popular web application for drawing and analysing DAGs. Here we introduce the R package ÔdagittyÕ, which provides access to all of the capabilities of the DAGitty web application within the R platform for statistical computing, and also offers several new functions. We describe how the R package ÔdagittyÕ can be used to: evaluate whether a DAG is consistent with the dataset it is intended to represent; enumerate Ôstatistically equivalentÕ but causally different DAGs; and identify exposure-outcome adjustment sets that are valid for causally different but statistically equivalent DAGs. This functionality enables epidemiologists to detect causal misspecifications in DAGs and make robust inferences that remain valid for a range of different DAGs. AvailabilityThe R package ÔdagittyÕ is available through the comprehensive R archive network (CRAN) at https://cran.r-project.org/web/packages/dagitty/. The source code is available on github at https://github.com/jtextor/dagitty. The web application ÔDAGittyÕ is free software, licensed under the GNU general public license (GPL) version 2 and is available at http://dagitty.net/.

Counting and uniform sampling of directed acyclic graphs (DAGs) from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper, we show that these tasks can be performed in polynomial time, solving a long-standing open problem in this area. Our algorithms are effective and easily implementable. Experimental results show that the algorithms significantly outperform state-of-the-art methods.

We study the role of connectivity of communication networks in private computations under information theoretic settings. It will be shown that some functions can be computed by private protocols even if the underlying network is 1-connected but not 2-connected. Then we give a complete characterisation of non-degenerate functions that can be computed on non-2-connected networks. Furthermore, a general technique for simulating private protocols on arbitrary networks will be presented. Using this technique every private protocol can be simulated on arbitrary k-connected networks using only a small number of additional random bits. Finally, we give matching lower and upper bounds for the number of random bits needed to compute the parity function on k-connected networks.On leave from Instytut Informatyki, Uniwersytet Wroc lawski, Poland.

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