1. G0 = G; h = 0; 2. while Gh has more than 2 vertices do randomly pick an edge eh in Gh; Gh+1 = Gh/eh; h = h+ 1; 3. return all edges in Gn−2. As we have shown in section 1, the probability Pr[Eh | h−1 i=1 Ei] that, under the condition that the first (h − 1)-st iterations of the algorithm do not pick an edge in the min-cut C of G, the probability that the h-th iteration does not pick an edge in...

In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games played on random geometric graphs. For each of our four games we show that if we add edges between n points chosen uniformly at random in the unit square by order of ...

Motivated by applications in online dating and kidney exchange, we study a stochastic matching problem in which we have a random graph G given by a node set V and probabilities p(i, j) on all pairs i, j ∈ V representing the probability that edge (i, j) exists. Additionally, each node has an integer weight t(i) called its patience parameter. Nodes represent agents in a matching market with dicho...

Graphs play an important role in modern world, due to their widespread use for modeling, representing and organizing linked data. Taking into consideration that most of the “killer” applications require a graph-based representation (e.g., the Web, social network management, protein-protein interaction networks), efficient query processing and analysis techniques are required, not only because t...

We study “tricolor percolation” on the regular tessellation of R by truncated octahedra, which is the three-dimensional analog of the hexagonal tiling of the plane. We independently assign one of three colors to each cell according to a probability vector p = (p1, p2, p3) and define a “tricolor edge” to be an edge incident to one cell of each color. The tricolor edges form disjoint loops and/or...

This note extends the analysis of incremental PageRank in [B. Bahmani, A. Chowdhury, and A. Goel. Fast Incremental and Personalized PageRank. VLDB 2011]. In that work, the authors prove a running time of O( 2 ln(m)) to keep PageRank updated over m edge arrivals in a graph with n nodes when the algorithm stores R random walks per node and the PageRank teleport probability is . To prove this runn...

We present an eecient method for maintaining mixtures of prunings of a prediction or decision tree that extends the previous methods for \node-based" prunings to the larger class of edge-based prunings. The method includes an online weight-allocation algorithm that can be used for prediction, compression and classiication. Although the set of edge-based prunings of a given tree is much larger t...

Certain dynamical systems, such as the shift map and the logistic map, have an edge of chaos in their parameter spaces. On one side of this edge, the dynamics are chaotic for many parameter values, on the other side of the edge they are periodic. We find that discrete-time dynamical systems with wavelet filtered feedback from the dynamical variable to the parameters are attracted to a narrow pa...

Fixing an irrational α ∈ (0, 1) we prove the 0-1 law for the random graph on [n] with the probability of {i, j} being an edge being essentially 1 |i−j|α .