CDC is collaborating with the U.S. Environmental Protection Agency to urge U.S. residents to pay attention to their local air quality during Air Quality Awareness Week, April 28–May 2, 2014. May also is Asthma Awareness Month, and May 6 is World Asthma Day. Asthma sufferers are particularly affected by air pollution. One in 12 U.S. residents (approximately 25.5 million persons) currently has as...

Last Time During the last lecture we completed an argument for a 2 1 d−1 ) lower bound for depth-d circuits for parity (PAR) using Hastad’s Switching Lemma [H̊as87], which stated that, for f : {0, 1} → {−1, 1}, if CNFwidth(f) = t, Pρ←Rp(DNFwidth(f ρ) = s) ≥ (7ps) We proved the Weak Switching Lemma, asserting a (40ps2) lower bound for this probability as opposed to the tighter bound given by the ...

Article history: Received 18 October 2007 Received in revised form 25 March 2008 Accepted 3 April 2008 Available online 12 April 2008

In this lecture, we look at various data structures to solve problems about static trees: given a static tree, we perform some preprocessing to construct our data structure, then use the data structure to answer queries about the tree. The three problems we look at in this lecture are range minimum queries (RMQ), lowest common ancestors (LCA), and level ancestor (LA); we will support all these ...

We care not only about the value of the minimum element, but also about the index k of the minimum element between A[i] and A[j]; given the index, it is easy to look up the actual value of the minimum element, so it is a more interesting problem to find the index of the minimum element between A[i] and A[j]. The range minimum query problem is not a tree problem, but it closely related to a tree...

9 Article history: 10 Received 16 July 2014 11 Received in revised form 2 April 2015 12 Accepted 25 April 2015 13 Available online xxxx 14