CS 264 : Beyond Worst - Case Analysis Lecture # 9 : A Taste Of Compressive Sensing ∗

The last several lectures proved that polynomial-time exact recovery is possible for instances of several NP -hard problems that satisfy some type of stability condition. Lecture #7 showed that the single-link++ algorithm, which searches over a restricted set of feasible solutions, and thus can return a suboptimal solution in worst-case instances, recovers the optimal clustering in stable k-median instances. Last lecture we showed that a linear programming relaxation, whose optimal solution is generally not an integral solution, recovers the optimal multiway cut in stable instances. Today’s lecture continues this theme of exact recovery via linear programming, but in a different problem domain: systems of linear equations.