# On Cyclic Solutions to the Min-Max Latency Multi-Robot Patrolling Problem

For the Euclidean version of the problem, for instance, combining our results with known results on Euclidean TSP, yields a PTAS for approximating an optimal cyclic solution, and it yields a $(2(1-1/k)+\varepsilon)$-approximation of the optimal unrestricted solution.

# How can classical multidimensional scaling go wrong?

While $D_l$ is not metric, when given as input to cMDS instead of $D$, it empirically results in solutions whose distance to $D$ does not increase when we increase the dimension and the classification accuracy degrades less than the cMDS solution.

# Approximation Algorithms for Multi-Robot Patrol-Scheduling with Min-Max Latency

The problem is NP-hard, as it has the traveling salesman problem as a special case (when $k=1$ and all sites have the same weight).

# Fréchet Distance for Uncertain Curves

We prove that both the upper and lower bound problems are NP-hard for the continuous Fr\'echet distance in several uncertainty models, and that the upper bound problem remains hard for the discrete Fr\'echet distance.

Computational Geometry

# Sparse Approximate Conic Hulls

Equivalently, given the matrix X, consider the problem of finding a small subset, S, of the columns of X such that the conic hull of S \eps-approximates the conic hull of the columns of X, i. e., the distance of every column of X to the conic hull of the columns of S should be at most an \eps-fraction of the angular diameter of X.

# Sparse Approximation via Generating Point Sets

]{#1\left({#2}\right)} \newcommand{\npoints}{n} \newcommand{\ballD}{\mathsf{b}} \newcommand{\dataset}{{P}} $For a set$\dataset$of$\npoints$points in the unit ball$\ballD \subseteq \Re^d$, consider the problem of finding a small subset$\algset \subseteq \dataset$such that its convex-hull$\eps\$-approximates the convex-hull of the original set.

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