arXiv subjects

Jonas Friemel

Publications and source records attributed to Jonas Friemel.

4 recordsLinked to original sources

arXiv2026

Tilt Automata: Gathering Particles With Uniform External Control

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 tiles of a polyomino with all particles reacting uniformly to an external force by moving as far as possible in one of the four axis-parallel directions until they hit the boundary. The goal is to choose a sequence of directions that moves all particles to a common position. Our results include a polynomial-time algorithm for gathering in a completely filled polyomino as well as hardness reductions for approximating shortest gathering sequences and for determining whether the particles in a partially filled polyomino can be gathered. We pay special attention to the impact of restricted geometry, particularly polyominoes without holes. As corollaries, we make progress on an open question from [Balanza-Martinez et al., SODA 2020] by showing that deciding whether a given position can be occupied remains NP-hard in polyominoes without holes and provide initial results on the parameterized complexity of tilt problems. Our results build on a connection we establish between tilt models and the theory of synchronizing automata.

cs.CG↗

arXiv2025

Tile Reconfiguration by a Finite Automaton

Shape formation is one of the most thoroughly studied problems in programmable matter and swarm robotics. However, in many models, the class of shapes that can be formed is highly restricted due to the particles' limited memory. In the hybrid model, an active agent with the computational power of a deterministic finite automaton can form shapes by lifting and placing passive tiles on the triangular lattice. We study the shape reconfiguration problem where the agent additionally has the ability to distinguish so-called target nodes from non-target nodes and needs to form a target shape from the initial tile configuration. We present a worst-case optimal $O(mn)$ algorithm for simply connected target shapes, where $m$ is the initial number of unoccupied target nodes and $n$ is the total number of tiles. Furthermore, we show how an agent can reconfigure a large class of target shapes with holes in $O(n^4)$ steps.

cs.DS↗

arXiv2025

Moving Matter: Using a Single, Simple Robot to Reconfigure a Connected Set of Building Blocks

We implement and evaluate different methods for the reconfiguration of a connected arrangement of tiles into a desired target shape, using a single active robot that can move along the tile structure. This robot can pick up, carry, or drop off one tile at a time, but it must maintain a single connected configuration at all times. Becker et al. (CCCG 2025) recently proposed an algorithm that uses histograms as canonical intermediate configurations, guaranteeing performance within a constant factor of the optimal solution if the start and target configuration are well-separated. We implement and evaluate this algorithm, both in a simulated and practical setting, using an inchworm type robot to compare it with two existing heuristic algorithms.

cs.RO↗

arXiv2025

Efficient Reconfiguration of Tile Arrangements by a Single Active Robot

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 active robot that can move on the tiles, remove individual tiles from a given location and physically move them to a new position by walking on the remaining configuration. The objective is to determine a schedule that minimizes the overall makespan, while keeping the tile configuration connected. We provide both negative and positive results. (1) We generalize the problem by introducing weighted movement costs, which can vary depending on whether tiles are carried or not, and prove that this variant is NP-hard. (2) We give a polynomial-time constant-factor approximation algorithm for the case of disjoint start and target bounding boxes, which additionally yields optimal carry distance for 2-scaled instances.

cs.CG↗