Cs 59000 Ctt Current Topics in Theoretical Cs Lecture 1

The use of randomness in designing algorithms that deal with large data sets can lead to vast improvements in performance compared to deterministic algorithms for the same problems. In this course we will be looking at a few computational models that use randomness as a means to finding efficient or super-efficient algorithms for various computational problems specific to graphs, error-correcting codes, strings or functions. What do we mean by ‘super-efficient algorithms’? An algorithm that takes inputs of size n and whose running time is polynomial in n is said to be efficient. Typically, algorithms required to always output the correct answer must at least read their entire input, so their running time is at least linear in the size of the input. In practice, when dealing with huge data, say graphs with millions of nodes, even linear time algorithms are considered too slow. Can we do anything in time better than linear, that is with partial (i.e. local) information about the input? The answer to this question is yes, as long we are willing to live with approximate solutions to our problems. What do we really mean by approximate solutions? Of course, the answer depends on the computational model we look at, and it is often the case that even defining the right computational model for the tasks and the data that one is interested in can be a challenging task. We start by describing some models of sublinear computation that not only have been successful in practice but that have also proved to be instrumental in many fundamental developments across theoretical CS.