We give tight bounds on the parallel complexity of some problems involving random graphs. Speci cally, we show that a Hamiltonian cycle, a breadth rst spanning tree, and a maximal...
Surprisingly, general search heuristics often solve combinatorial problems quite sufficiently, although they do not outperform specialized algorithms. Here, the behavior of simple...
We consider the deterministic and the randomized decision tree complexities for Boolean functions, denoted DC(f) and RC(f), respectively. A major open problem is how small RC(f) ca...
We study the problem of local search on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a v...
We study the spectral norm of matrices M that can be factored as M = BA, where A is a random matrix with independent mean zero entries and B is a fixed matrix. Under the (4 + )-th ...