Tight Bounds for Asymptotic and Approximate Consensus

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a common value ...

In the d-dimensional bin packing problem (VBP), one is given vectors x₁,x₂, ... ,x_n ∈ R^d and the goal is to find a partition into a minimum number of feasible sets: {1,2 ... ,n} = ∪_i^s B_i. A set B_i is feasible if ∑_{j ∈ Bi} x_j ≤ 1, where 1 denotes the all 1'...

Suppose Alice holds a uniformly random string X ∈ {0, 1}^N and Bob holds a noisy version Y of X where each bit of X is flipped independently with probability ε ∈ [0, 1/2]. Alice and Bob would like to extract a common random string of min-entropy at least ...