arXiv subjects

Arne Schmidt

Publications and source records attributed to Arne Schmidt.

At least 19 recordsLinked to original sources

arXiv2026

Pass the Bucket: Efficient, Robust, Local Load Balancing for Teams of Heterogeneous Robots

We study the problem of decentralized, self-organized task sharing for a swarm of heterogeneous robots that collaborate in transportation or other objectives that require coordinated motion planning. To this end, we present theoretical and practical results for the simple but effective mechanism of \emph{bucket brigades} for load balancing, in which a team of heterogenous robots share a spatial task in a confined, one-dimensional space, while only being able to sense collisions with neighbors or walls. The goal is to optimize throughput of the overall system, without central control or information, aiming at an interval partition proportional to robot velocities. We address possible chaotic system behavior by developing a stabilization mechanism based on simple local aid, a ``token'', that temporarily decelerates robots after an encounter. This purely local change eliminates persistent oscillations, resulting in convergence towards a stable system state. We accelerate system convergence by comparing a single boundary token to ubiquitous two-directional tokens and optimizing the deceleration factor. Event-driven simulations report convergence times and robustness: For a large variety of perturbations (such as robot deletion, position or velocity jittering), the system reliably re-converges. The results suggest a local, practical mechanism for robust load balancing for heterogeneous teams of robots that promises an effective tool as basis for more complex scenarios.

cs.RO↗

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↗

arXiv2024

Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform External Forces

We investigate algorithmic approaches for targeted drug delivery in a complex, maze-like environment, such as a vascular system. The basic scenario is given by a large swarm of micro-scale particles (''agents'') and a particular target region (''tumor'') within a system of passageways. Agents are too small to contain on-board power or computation and are instead controlled by a global external force that acts uniformly on all particles, such as an applied fluidic flow or electromagnetic field. The challenge is to deliver all agents to the target region with a minimum number of actuation steps. We provide a number of results for this challenge. We show that the underlying problem is NP-complete, which explains why previous work did not provide provably efficient algorithms. We also develop several algorithmic approaches that greatly improve the worst-case guarantees for the number of required actuation steps. We evaluate our algorithmic approaches by numerous simulations, both for deterministic algorithms and searches supported by deep learning, which show that the performance is practically promising.

cs.CG↗

arXiv2024

Focused Active Learning for Histopathological Image Classification

Active Learning (AL) has the potential to solve a major problem of digital pathology: the efficient acquisition of labeled data for machine learning algorithms. However, existing AL methods often struggle in realistic settings with artifacts, ambiguities, and class imbalances, as commonly seen in the medical field. The lack of precise uncertainty estimations leads to the acquisition of images with a low informative value. To address these challenges, we propose Focused Active Learning (FocAL), which combines a Bayesian Neural Network with Out-of-Distribution detection to estimate different uncertainties for the acquisition function. Specifically, the weighted epistemic uncertainty accounts for the class imbalance, aleatoric uncertainty for ambiguous images, and an OoD score for artifacts. We perform extensive experiments to validate our method on MNIST and the real-world Panda dataset for the classification of prostate cancer. The results confirm that other AL methods are 'distracted' by ambiguities and artifacts which harm the performance. FocAL effectively focuses on the most informative images, avoiding ambiguities and artifacts during acquisition. For both experiments, FocAL outperforms existing AL approaches, reaching a Cohen's kappa of 0.764 with only 0.69% of the labeled Panda data.

cs.CV↗

arXiv2023

Introducing instance label correlation in multiple instance learning. Application to cancer detection on histopathological images

In the last years, the weakly supervised paradigm of multiple instance learning (MIL) has become very popular in many different areas. A paradigmatic example is computational pathology, where the lack of patch-level labels for whole-slide images prevents the application of supervised models. Probabilistic MIL methods based on Gaussian Processes (GPs) have obtained promising results due to their excellent uncertainty estimation capabilities. However, these are general-purpose MIL methods that do not take into account one important fact: in (histopathological) images, the labels of neighboring patches are expected to be correlated. In this work, we extend a state-of-the-art GP-based MIL method, which is called VGPMIL-PR, to exploit such correlation. To do so, we develop a novel coupling term inspired by the statistical physics Ising model. We use variational inference to estimate all the model parameters. Interestingly, the VGPMIL-PR formulation is recovered when the weight that regulates the strength of the Ising term vanishes. The performance of the proposed method is assessed in two real-world problems of prostate cancer detection. We show that our model achieves better results than other state-of-the-art probabilistic MIL methods. We also provide different visualizations and analysis to gain insights into the influence of the novel Ising term. These insights are expected to facilitate the application of the proposed model to other research areas.

cs.CV↗

arXiv2023

Probabilistic Modeling of Inter- and Intra-observer Variability in Medical Image Segmentation

Medical image segmentation is a challenging task, particularly due to inter- and intra-observer variability, even between medical experts. In this paper, we propose a novel model, called Probabilistic Inter-Observer and iNtra-Observer variation NetwOrk (Pionono). It captures the labeling behavior of each rater with a multidimensional probability distribution and integrates this information with the feature maps of the image to produce probabilistic segmentation predictions. The model is optimized by variational inference and can be trained end-to-end. It outperforms state-of-the-art models such as STAPLE, Probabilistic U-Net, and models based on confusion matrices. Additionally, Pionono predicts multiple coherent segmentation maps that mimic the rater's expert opinion, which provides additional valuable information for the diagnostic process. Experiments on real-world cancer segmentation datasets demonstrate the high accuracy and efficiency of Pionono, making it a powerful tool for medical image analysis.

eess.IV↗

arXiv2023

Computing Motion Plans for Assembling Particles with Global Control

We investigate motion planning algorithms for the assembly of shapes in the \emph{tilt model} in which unit-square tiles move in a grid world under the influence of uniform external forces and self-assemble according to certain rules. We provide several heuristics and experimental evaluation of their success rate, solution length, runtime, and memory consumption.

cs.RO↗

arXiv2023

Probabilistic Attention based on Gaussian Processes for Deep Multiple Instance Learning

Multiple Instance Learning (MIL) is a weakly supervised learning paradigm that is becoming increasingly popular because it requires less labeling effort than fully supervised methods. This is especially interesting for areas where the creation of large annotated datasets remains challenging, as in medicine. Although recent deep learning MIL approaches have obtained state-of-the-art results, they are fully deterministic and do not provide uncertainty estimations for the predictions. In this work, we introduce the Attention Gaussian Process (AGP) model, a novel probabilistic attention mechanism based on Gaussian Processes for deep MIL. AGP provides accurate bag-level predictions as well as instance-level explainability, and can be trained end-to-end. Moreover, its probabilistic nature guarantees robustness to overfitting on small datasets and uncertainty estimations for the predictions. The latter is especially important in medical applications, where decisions have a direct impact on the patient's health. The proposed model is validated experimentally as follows. First, its behavior is illustrated in two synthetic MIL experiments based on the well-known MNIST and CIFAR-10 datasets, respectively. Then, it is evaluated in three different real-world cancer detection experiments. AGP outperforms state-of-the-art MIL approaches, including deterministic deep learning ones. It shows a strong performance even on a small dataset with less than 100 labels and generalizes better than competing methods on an external test set. Moreover, we experimentally show that predictive uncertainty correlates with the risk of wrong predictions, and therefore it is a good indicator of reliability in practice. Our code is publicly available.

cs.LG↗

arXiv2022

Efficiently Reconfiguring a Connected Swarm of Labeled Robots

When considering motion planning for a swarm of $n$ labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel, collision-free robot motions. The objective is to reach the new configuration in a minimum amount of time; an important constraint is to keep the swarm connected at all times. Problems of this type have been considered before, with recent notable results achieving constant stretch for not necessarily connected reconfiguration: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of $d$, the total duration of an overall schedule can be bounded to $\mathcal{O}(d)$, which is optimal up to constant factors. However, constant stretch could only be achieved if disconnected reconfiguration is allowed, or for scaled configurations (which arise by increasing all dimensions of a given object by the same multiplicative factor) of unlabeled robots. We resolve these major open problems by (1) establishing a lower bound of $\Omega(\sqrt{n})$ for connected, labeled reconfiguration and, most importantly, by (2) proving that for scaled arrangements, constant stretch for connected reconfiguration can be achieved. In addition, we show that (3) it is NP-complete to decide whether a makespan of 2 can be achieved, while it is possible to check in polynomial time whether a makespan of 1 can be achieved.

cs.CG↗

arXiv2022

Particle-Based Assembly Using Precise Global Control

In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is constructible. Previous work provides a class of shapes for which constructibility can be decided efficiently when particles move maximally into the same direction induced by a global signal. In this paper we consider the single step model, i.e., a model in which each particle moves one unit step into the given direction. We restrict the assembly process such that at each single time step actually one particle is added to and moved within the workspace. We prove that deciding constructibility is NP-complete for three-dimensional shapes, and that a maximum constructible shape can be approximated. The same approximation algorithm applies for 2D. We further present linear-time algorithms to decide whether or not a tree-shape in 2D or 3D is constructible. Scaling a shape yields constructibility; in particular we show that the $2$-scaled copy of every non-degenerate polyomino is constructible. In the three-dimensional setting we show that the $3$-scaled copy of every non-degenerate polycube is constructible.

cs.CG↗

arXiv2021

Computing Area-Optimal Simple Polygonizations

We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical methods have received considerable attention. However, previous methods focused on heuristic methods, with no proof of optimality. We develop exact methods, based on a combination of geometry and integer programming. As a result, we are able to solve instances of up to n=25 points to provable optimality. While this extends the range of solvable instances by a considerable amount, it also illustrates the practical difficulty of both problem variants.

cs.CG↗

arXiv2019

Parallel Online Algorithms for the Bin Packing Problem

We study \emph{parallel} online algorithms: For some fixed integer $k$, a collective of $k$ parallel processes that perform online decisions on the same sequence of events forms a $k$-\emph{copy algorithm}. For any given time and input sequence, the overall performance is determined by the best of the $k$ individual total results. Problems of this type have been considered for online makespan minimization; they are also related to optimization with \emph{advice} on future events, i.e., a number of bits available in advance. We develop \textsc{Predictive Harmonic}$_3$ (PH3), a relatively simple family of $k$-copy algorithms for the online Bin Packing Problem, whose joint competitive factor converges to 1.5 for increasing $k$. In particular, we show that $k=6$ suffices to guarantee a factor of $1.5714$ for PH3, which is better than $1.57829$, the performance of the best known 1-copy algorithm \textsc{Advanced Harmonic}, while $k=11$ suffices to achieve a factor of $1.5406$, beating the known lower bound of $1.54278$ for a single online algorithm. In the context of online optimization with advice, our approach implies that 4 bits suffice to achieve a factor better than this bound of $1.54278$, which is considerably less than the previous bound of 15 bits.

cs.DS↗

arXiv2019

Connected Assembly and Reconfiguration by Finite Automata

We consider methods for connected reconfigurations by finite automate in the so-called \emph{hybrid} or \emph{Robot-on-Tiles} model of programmable matter, in which a number of simple robots move on and rearrange an arrangement of passive tiles in the plane that form \emph{polyomino} shapes, making use of a supply of additional tiles that can be placed. We investigate the problem of reconfiguration under the constraint of maintaining connectivity of the tile arrangement; this reflects scenarios in which disconnected subarrangements may drift apart, e.g., in the absence of gravity in space. We show that two finite automata suffice to mark a bounding box, which can then be used as a stepping stone for more complex operations, such as scaling a tile arrangement by a given factor, rotating arrangements, or copying arrangements to a different location. We also describe an algorithm for scaling monotone polyominoes without the help of a bounding box.

cs.CG↗

arXiv2018

CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata

We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store significant amounts of data, nor perform complex computations, and is limited to a handful of possible physical operations. We provide a toolbox for carrying out fundamental tasks on a given arrangement of tiles, using the arrangement itself as a storage device, similar to a higher-dimensional Turing machine with geometric properties. Specific results include time- and space-efficient procedures for bounding, counting, copying, reflecting, rotating or scaling a complex given shape.

cs.DS↗

arXiv2018

Efficient Parallel Self-Assembly Under Uniform Control Inputs

We prove that by successively combining subassemblies, we can achieve sublinear construction times for "staged" assembly of micro-scale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance in the context of programmable matter and self-assembly for building high-yield micro-factories.The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles bond when forced together with a compatible particle. Previous work considered sequential composition of objects, resulting in construction time that is linear in the number N of particles, which is inefficient for large N. Our progress implies critical speedup for constructible shapes; for convex polyominoes, even a constant construction time is possible. We also show that our construction process can be used for pipelining, resulting in an amortized constant production time.

cs.CG↗

arXiv2018

Don't Rock the Boat: Algorithms for Balanced Dynamic Loading and Unloading

We consider dynamic loading and unloading problems for heavy geometric objects. The challenge is to maintain balanced configurations at all times: minimize the maximal motion of the overall center of gravity. While this problem has been studied from an algorithmic point of view, previous work only focuses on balancing the final center of gravity; we give a variety of results for computing balanced loading and unloading schemes that minimize the maximal motion of the center of gravity during the entire process. In particular, we consider the one-dimensional case and distinguish between loading and unloading. In the unloading variant, the positions of the intervals are given, and we search for an optimal unloading order of the intervals. We prove that the unloading variant is NP-complete and give a 2.7-approximation algorithm. In the loading variant, we have to compute both the positions of the intervals and their loading order. We give optimal approaches for several variants that model different loading scenarios that may arise, e.g., in the loading of a transport ship with containers.

cs.CG↗

arXiv2017

Tilt Assembly: Algorithms for Micro-Factories That Build Objects with Uniform External Forces

We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield micro-factories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles can bond when being forced together with another appropriate particle. Due to the physical and geometric constraints, not all shapes can be built in this manner; this gives rise to the Tilt Assembly Problem (TAP) of deciding constructibility. For simply-connected polyominoes $P$ in 2D consisting of $N$ unit-squares ("tiles"), we prove that TAP can be decided in $O(N\log N)$ time. For the optimization variant MaxTAP (in which the objective is to construct a subshape of maximum possible size), we show polyAPX-hardness: unless P=NP, MaxTAP cannot be approximated within a factor of $Ω(N^{\frac{1}{3}})$; for tree-shaped structures, we give an $O(N^{\frac{1}{2}})$-approximation algorithm. For the efficiency of the assembly process itself, we show that any constructible shape allows pipelined assembly, which produces copies of $P$ in $O(1)$ amortized time, i.e., $N$ copies of $P$ in $O(N)$ time steps. These considerations can be extended to three-dimensional objects: For the class of polycubes $P$ we prove that it is NP-hard to decide whether it is possible to construct a path between two points of $P$; it is also NP-hard to decide constructibility of a polycube $P$. Moreover, it is expAPX-hard to maximize a path from a given start point.

cs.DS↗