Beyond worst-case analysis Page 1 88 COMMUNICATIONS OF THE ACM | MARCH 2019 |
VOL. 62 | NO. 3 review articles COMPARING DIFFERENT ALGORITHMS is hard. For almost …

Much of modern learning theory has been split between two regimes: the classical offline
setting, where data arrive independently, and the online setting, where data arrive …

We study algorithmic problems that belong to the complexity class of the existential theory of
the reals (∃R). A problem is\ensuremath ∃\mathbbR-complete if it is as hard as the …

We consider (i) the problem of finding a (possibly mixed) Nash equilibrium in congestion
games, and (ii) the problem of finding an (exponential precision) fixed point of the gradient …

In 1988, Johnson, Papadimitriou and Yannakakis wrote that" Practically all the empirical
evidence would lead us to conclude that finding locally optimal solutions is much easier than …

Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound
connections to the complexity of the fundamental cryptographic primitives: collision-resistant …

Banach's fixed point theorem for contraction maps has been widely used to analyze the
convergence of iterative methods in non-convex problems. It is a common experience …

We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most φ n
O (√ log n), where n is the number of nodes in the graph and φ is a parameter that …

Metaheuristics provide high-level instructions for designing heuristic optimisation algorithms
and have been successfully applied to a range of computationally hard real-world problems …

Worst-case hardness results for most equilibrium computation problems have raised the
need for beyond-worst-case analysis. To this end, we study the smoothed complexity of …