Subset Sum algorithm, why not split by 3+?
First of all, let me mention that the algorithm you mention is attributed to Horowitz and Sahni (1974), whose algorithm achieves time $O(2^{n/2})$ and space $O(2^{n/2})$. A major improvement due to Schroeppel and Shamir (1981) reduces memory consumption to $O(2^{n/4})$ while keeping the same running time; this algorithm divides the input into four sets.

The topic is of interest to cryptographers, and there has been a recent line of improvements: Howgrave-Graham and Joux (2010), Becker, Coron and Joux (2011), Dinur, Dunkelman, Keller and Shamir (2012) and Austrin, Kaski, Koivisto and Määttä (2013), which seems to be the latest word on the subject; the authors of the last paper are actually not cryptographers.