Adversarial smoothed analysis

Minicourse on Smoothed Analysis

Introduction to Smoothed Analysis

We consider the knapsack problem. There are n items, each with a weight wi > 0 and with a profit pi > 0, and a capacity bound W > 0. Our task is to find a subset S of the items so as to maximize the overall profit ∑ i∈S pi while not exceeding the capacity bound, i.e., ∑ i∈S wi ≤ W . It is well known that the knapsack problem is NP-hard. So, unless P = NP , there is no polynomial-time algorithm....

Adversarial classification: An adversarial risk analysis approach

Classification problems in security settings are usually contemplated as confrontations in which one or more adversaries try to fool a classifier to obtain a benefit. Most approaches to such adversarial classification problems have focused on game theoretical ideas with strong underlying common knowledge assumptions, which are actually not realistic in security domains. We provide an alternativ...

Smoothed Analysis on Connected Graphs

The main paradigm of smoothed analysis on graphs suggests that for any large graph G in a certain class of graphs, perturbing slightly the edges of G at random (usually adding few random edges to G) typically results in a graph having much “nicer” properties. In this work we study smoothed analysis on trees or, equivalently, on connected graphs. Given an n-vertex connected graph G, form a rando...

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...