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A Sublinear Approximation Algorithm for Minimum Dilation Trees in the Plane
Sarita de Berg, Jacobus Conradi, Peter Kramer +2
The dilation of a geometric graph measures how much longer the path between pairs of points becomes when restricted to graph edges, rather than following the direct path through th…
Central Triangulation under Parallel Flip Operations: The CG:SHOP Challenge 2026
Oswin Aichholzer, Joseph Dorfer, Sándor P. Fekete +3
We give an overview of the 2026 Computational Geometry Challenge targeting the problem of finding a Central Triangulation under Parallel Flip Operations in triangulations of point…
Minimum Exposure Motion Planning
Sarita de Berg, Joachim Gudmundsson, Peter Kramer +2
We investigate multiple fundamental variants of the classic coordinated motion planning (CMP) problem for unit square robots in the plane under the metric. In coordinated mot…
Sliding Cubes in Parallel
Hugo A. Akitaya, Joseph Dorfer, Peter Kramer +3
We study the classic sliding cube model for programmable matter under parallel reconfiguration in three dimensions, providing novel algorithmic and surprising complexity results in…
Structural Properties of Shortest Flip Sequences Between Plane Spanning Trees
Oswin Aichholzer, Joseph Dorfer, Peter Kramer +2
We study the reconfiguration of plane spanning trees on point sets in the plane in convex position, where a reconfiguration step (flip) replaces one edge with another, yielding aga…
Tilt Automata: Gathering Particles With Uniform External Control
Sándor P. Fekete, Jonas Friemel, Peter Kramer +3
Motivated by targeted drug delivery, we investigate the gathering of particles in the full tilt model of externally controlled motion planning: A set of particles is located at the…
Drainability and Fillability of Polyominoes in Diverse Models of Global Control
Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt +2
Tilt models offer intuitive and clean definitions of complex systems in which particles are influenced by global control commands. Despite a wide range of applications, there has b…
Efficient Reconfiguration of Tile Arrangements by a Single Active Robot
Aaron T. Becker, Sándor P. Fekete, Jonas Friemel +6
We consider the problem of reconfiguring a two-dimensional connected grid arrangement of passive building blocks from a start configuration to a goal configuration, using a single…
Sliding Squares in Parallel
Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer +4
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given square-shaped modules in a (labeled or unlabele…
Coordinated Motion Planning: Multi-Agent Path Finding in a Densely Packed, Bounded Domain
Sándor P. Fekete, Ramin Kosfeld, Peter Kramer +3
We study Multi-Agent Path Finding for arrangements of labeled agents in the interior of a simply connected domain: Given a unique start and target position for each agent, the goal…
On the Connectivity of the Flip Graph of Plane Spanning Paths
Linda Kleist, Peter Kramer, Christian Rieck
Flip graphs of non-crossing configurations in the plane are widely studied objects, e.g., flip graph of triangulations, spanning trees, Hamiltonian cycles, and perfect matchings. T…
Efficiently Reconfiguring a Connected Swarm of Labeled Robots
Sándor P. Fekete, Peter Kramer, Christian Rieck +2
When considering motion planning for a swarm of labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel,…