We present an algorithm for maintaining a maximal matching in a graph under addition and deletion of edges. Our algorithm is randomized and it takes expected amortized O(log n) time for each edge update where n is the number of vertices in the graph. Moreover, for any sequence of t edge updates, the total time taken by the algorithm is O(t log n + n log 2 n) with high probability. Note:The previous version of this result appeared in SIAM J. Comp., 44(1): 88-113, 2015. However, the analysis presented there for the algorithm was erroneous. This version rectifies this deficiency without any changes in the algorithm while preserving the performance bounds of the original algorithm.

We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a (1 + ǫ) approximation of maximum matching under edge insertions/deletions in worst case O( √ mǫ −2 ) time per update. This improves the 3/2 approximation given in [Neiman, Solomon,STOC 2013] which runs in similar time. The result is based on two ideas. The first is to re-run a static algorithm after a chosen number of updates to ensure approximation guarantees. The second is to judiciously trim the graph to a smaller equivalent one whenever possible. We also study extensions of our approach to the weighted setting, and combine it with known frameworks to obtain arbitrary approximation ratios. For a constant ǫ and for graphs with edge weights between 1 and N , we design an algorithm that maintains an (1 + ǫ)-approximate maximum weighted matching in O( √ m log N ) time per update. The only previous result for maintaining weighted matchings on dynamic graphs has an approximation ratio of 4.9108, and was shown in [Anand, Baswana, Gupta, Sen, FSTTCS 2012, arXiv 2012].

We present an algorithm for maintaining a maximal matching in a graph under addition and deletion of edges. Our algorithm is randomized and it takes expected amortized O(log n) time for each edge update where n is the number of vertices in the graph. Moreover, for any sequence of t edge updates, the total time taken by the algorithm is O(t log n + n log 2 n) with high probability. Note:The previous version of this result appeared in SIAM J. Comp., 44(1): 88-113, 2015. However, the analysis presented there for the algorithm was erroneous. This version rectifies this deficiency without any changes in the algorithm while preserving the performance bounds of the original algorithm.

Evidence-based medicine (EBM) is a concept that has grown to dominate the medical literature over the last decade. EBM has provoked a variety of criticisms, scientific, philosophical and sociological. However, while its basic conclusion--that we should practise EBM--is ethical, there has been limited ethical analysis of EBM. This paper aims to provide an analysis of EBM from an ethical perspective and identify some of EBM's potential ethical implications. Following a description of what constitutes EBM, this paper will identify and assess some of the basic values and epistemological assumptions of EBM that provide support for the moral duty to practise EBM. It will then examine potential ethical implications that could arise from practising EBM, given the challenges that have been made of EBM's assumptions and claims to authority. This paper will conclude by arguing that practitioners could strengthen the ethics of EBM by embracing a broader definition of evidence and including ethical criteria in the critical appraisal of research studies.