Approximation Algorithms That Take Advice
Many recently designed approximation algorithms use a simple but apparently powerful idea. The algorithm is allowed to ask a trusted oracle for a small number (say O(log n)) bits of “advice” For instance, it could ask for O(log n) bits of the optimum answer. Of course, strictly speaking, a polynomial-time algorithm has no need for log n bits of advice: it could just try all possibilities for this advice and retain the one that works the best. Nevertheless, this is a useful way of thinking about some approximation algorithms. In the talk I will present a few examples. My title is a play on the title of a classic paper on nonuniform computation “Turing Machines that take advice” (Karp and Lipton 1982).