## computer science posts

• 21 Nov 2017 » The Johnson-Lindenstrauss Lemma

The so-called curse of dimensionality reflects the idea that many methods are more difficult in higher-dimensions. This difficulty may be due a number of issues that become more complicated in higher-dimensions…

• 05 Nov 2017 » Online decision making under total uncertainty

In this post, we will discuss a few simple algorithms for online decision making with expert advice. In particular, this setting assumes no prior distribution on the set of outcomes, but we use hindsight to improve future decisions. The algorithms discussed include a simple deterministic and randomized majority weighted decision algorithm, and the multiplicative weights algorithm….

• In this post, we’ll review linear systems and linear programming. We’ll then focus on how to use LP relaxations to provide approximate solutions to other (binary integer) problems that are NP-hard….

• 29 Dec 2014 » Perfect Hashing with a 2-Universal Hash Family

Previously, we discussed universal hash families. In this post, we discuss a method of using a 2-universal hash family along with a Las Vegas algorithm to allow for perfect hashing, where the time required to find an item in a hash table is constant….

• 06 Sep 2014 » Universal hash functions

Hashing is a general method of reducing the size of a set by reindexing the elements into $$n$$ bins. This is done using a hash function, which maps some set $$U$$ into a range $$[0, n-1]$$. When designing a hash function, we are interested in something that maps elements into a bin in a way that appears random….