Equivalence classes and conditional hardness in massively parallel computations.

The (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.

New Tools and Connections for Exponential-Time Approximation.

In this paper, we develop new tools and connections for . In this setting, we are given a problem instance and an integer , and the goal is to design an approximation algorithm with the fastest possible running time. We give randomized algorithms that establish an approximation ratio of for maximum independent set in time, for chromatic number in time, for minimum vertex cover in time, and for minimum -hypergraph vertex cover in time.