A random graph order, also known as a transitive percolation process, is defined by taking a random graph on the vertex set {0, . . . , n − 1}, and putting i below j if there i...
Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from [16, 17] finds a satisfying assignment of Φ in pol...
This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level O...
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivati...