Nature Reserve Selection Problem: A Tight Approximation Algorithm

A Near-Tight Approximation Algorithm for the Robot Localization Problem

Localization is a fundamental problem in robotics. The “kidnapped robot” possesses a compass and map of its environment; it must determine its location at a minimum cost of travel distance. The problem is NP-hard [G. Dudek, K. Romanik, and S. Whitesides, SIAM J. Comput., 27 (1998), pp. 583–604] even to minimize within factor c logn [C. Tovey and S. Koenig, Proceedings of the National Conference...

An improved approximation algorithm for the column subset selection problem

We consider the problem of selecting the “best” subset of exactly k columns from an m× n matrix A. In particular, we present and analyze a novel two-stage algorithm that runs in O(min{mn2,m2n}) time and returns as output an m × k matrix C consisting of exactly k columns of A. In the first stage (the randomized stage), the algorithm randomly selects O(k log k) columns according to a judiciously-...

Tight Approximation Algorithm for Connectivity Augmentation Problems

The S-connectivity λG(u, v) of (u, v) in a graph G is the maximum number of uv-paths that no two of them have an edge or a node in S − {u, v} in common. The corresponding Connectivity Augmentation (CA) problem is: given a graph G0 = (V,E0), S ⊆ V , and requirements r(u, v) on V ×V , find a minimum size set F of new edges (any edge is allowed) so that λSG0+F (u, v) ≥ r(u, v) for all u, v ∈ V . E...

Spatially-Correlated Risk in Nature Reserve Site Selection

Establishing nature reserves protects species from land cover conversion and the resulting loss of habitat. Even within a reserve, however, many factors such as fires and defoliating insects still threaten habitat and the survival of species. To address the risk to species survival after reserve establishment, reserve networks can be created that allow some redundancy of species coverage to max...

The Algorithm Selection Problem