We consider the problem of sequentially learning good alternatives from among a pool, but with only relative utility feedback from adaptively chosen subsets.

Abstract: Schaffer and Yannakakis have shown that the max-cut problem with the FLIP neighborhood is polynomial-time local search (PLS) complete, and hence among the most difficult problems in the PLS class.

Abstract: I will provide an account of my research in various areas. As an exemplar, I will discuss the first two topics in greater detail.

Abstract: PCP Theorem characterizes the class NP and gives hardness of approximation for many optimization problems. Despite this, several tight hardness of approximation results remain elusive via the PCP theorem.