# Semi-dynamic Connectivity in the Plane

@inproceedings{Cabello2015SemidynamicCI, title={Semi-dynamic Connectivity in the Plane}, author={Sergio Cabello and Michael Kerber}, booktitle={WADS}, year={2015} }

Motivated by a path planning problem we consider the following procedure. Assume that we have two points $s$ and $t$ in the plane and take $\mathcal{K}=\emptyset$. At each step we add to $\mathcal{K}$ a compact convex set that does not contain $s$ nor $t$. The procedure terminates when the sets in $\mathcal{K}$ separate $s$ and $t$. We show how to add one set to $\mathcal{K}$ in $O(1+k\alpha(n))$ amortized time plus the time needed to find all sets of $\mathcal{K}$ intersecting the newly added…

## 3 Citations

### Soft Subdivision Search in Motion Planning, II: Axiomatics

- Computer ScienceFAW
- 2015

This paper addresses the issue of subdivision in non-Euclidean configuration spaces, and how exact algorithms can be recovered using soft methods, and provides a general axiomatic theory underlying these results.

### Soft Subdivision Search in Motion Planning, II: Axiomatics

- Computer Science
- 2018

This paper addresses the issue of subdivision in non-Euclidean configuration spaces, and how exact algorithms can be recovered using soft methods, and provides a general axiomatic theory underlying these results.

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