Smoothed analysis of κ(A)

Smoothed Analysis of Probabilistic Roadmaps

The probabilistic roadmap algorithm is a leading heuristic for robot motion planning. It is extremely efficient in practice, yet its worst case convergence time is unbounded as a function of the input’s combinatorial complexity. We prove a smoothed polynomial upper bound on the number of samples required to produce an accurate probabilistic roadmap, and thus on the running time of the algorithm...

Minicourse on Smoothed Analysis

Smoothed Analysis of Balancing Networks

In a load balancing network each processor has an initial collection of unit-size jobs, tokens, and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to some predefined rule. As it turns out, this rule crucially effects the performance of the network. In this work we propose a model that studies this ef...

Smoothed Analysis of Linear Programming

1 Und die Bewegung in den Rosen, sieh: Gebärden von so kleinem Ausschlagswinkel, daß sie unsichtbar blieben, liefen ihre Strahlen nicht auseinander in das Weltall.

Smoothed Analysis of Condition Numbers

The running time of many iterative numerical algorithms is dominated by the condition number of the input, a quantity measuring the sensitivity of the solution with regard to small perturbations of the input. Examples are iterative methods of linear algebra, interior-point methods of linear and convex optimization, as well as homotopy methods for solving systems of polynomial equations. Thus a ...