Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube Bn = {0, 1}n with nearest neighbor edges. For oriented and unoriented percolation, p = e/n and p = 1/n are the respective critical probabilities. For oriented first-passage percolation with i.i.d. edge-passage times having a density of 1 near the origin, the percolation time (time to reach the o...

Given a graph G on n vertices with maximal degree d, form a random subgraph Gp by choosing each edge of G independently with probability p. Strengthening a classical result of Margulis we prove that if the edge connectivity k(G) satisfies k(G) À d/ log n, then the connectivity threshold in Gp is sharp. This result is asymptotically tight.

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

We present a randomized algorithm for dynamic graph connectivity. With failure probability less than 1/n (for any constant c we choose), our solution has worst case running time O(log n) per edge insertion, O(log n) per edge deletion, and O(log n/ log log n) per query, where n is the number of vertices. The previous best algorithm has worst case running time O(log n) per edge insertion and O(lo...

In this paper we introduce a novel algorithm for incorporating uncertainty into lookahead planning. Our algorithm searches through connected graphs with uncertain edge costs represented by known probability distributions. As a robot moves through the graph, the true edge costs of adjacent edges are revealed to the planner prior to traversal. This locally revealed information allows the planner ...

We describe and evaluate several methods for estimating the confidence in the per-edge correctness of a predicted dependency parse. We show empirically that the confidence is associated with the probability that an edge is selected correctly and that it can be used to detect incorrect edges very efficiently. We evaluate our methods on parsing text in 14 languages.