Alexandre Stauffer

Balls-into-bins with nearly optimal load distribution

We consider sequential balls-into-bins processes that randomly allocate m balls into n bins. We analyze two allocation schemes that achieve a close to optimal maximum load of ⌈m/n⌉ + 1 and require only O(m) (expected) allocation time. These parameters should be compared with the classic d-choice-process which achieves a maximum load of m/n + log log n/d + O(1) and requires m • d allocation time.

Balls into bins via local search

We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. In our main result, we prove that this process yields a maximum load of only Θ(log log n) on expander graphs. In addition, we show that for d-dimensional grids the maximum load is Θ((log n/log log n) 1/d+1). Finally, for almost regular graphs with minimum degree Ω(log n), we prove that the maximum load is constant and also reveal a fundamental difference between random and arbitrary tie-breaking rules.

Dynamics of lattice triangulations on thin rectangles

We consider random lattice triangulations of

Space-time percolation and detection by mobile nodes

n\times k

Dissemination strategy for immunizing scale-free networks.

rectangular regions with weight

Randomized Rumor Spreading in Dynamic Graphs

\lambda^{|\sigma|}

Balls into bins via local search: Cover time and maximum load

where

Diameter and broadcast time of random geometric graphs in arbitrary dimensions

\lambda>0

Critical density of activated random walks on transitive graphs

is a parameter and

Intersection and mixing times for reversible chains

|\sigma|