Alias tables are pretty cool, I wrote an interactive visualization of how they get built as part of this post a while ago: http://engineering.flipboard.com/2017/02/storyclustering . We used alias tables with MCMC and the hastings metropolis test to build a super fast LDA.
Also worth reading up on are sum-heaps. Alias tables are O(1) to sample from but O(n) to build/modify. Sum-heaps let you modify in O(log(n)) at the cost of sampling in O(log(n)) as well. A good writeup is here: https://timvieira.github.io/blog/post/2016/11/21/heaps-for-i...