Sándor P. Fekete’s research while affiliated with Klinikum Braunschweig and other places

Degree distributions in protein-protein interaction (PPI) networks are believed to follow a power law (PL). However, technical and study bias affect the experimental procedures for detecting PPIs. For instance, cancer-associated proteins have received disproportional attention. Moreover, bait proteins in large-scale experiments tend to have many false-positive interaction partners. Studying the degree distributions of thousands of PPI networks of controlled provenance, we address the question if PL distributions in observed PPI networks could be explained by these biases alone. Our findings are supported by mathematical models and extensive simulations and indicate that study bias and technical bias suffice to produce the observed PL distribution. It is, hence, problematic to derive hypotheses about the topology of the true biological interactome from the PL distributions in observed PPI networks. Our study casts doubt on the use of the PL property of biological networks as a modeling assumption or quality criterion in network biology.

We consider algorithmic problems motivated by modular robotic reconfiguration, for which we are given n square-shaped modules (or robots) in a (labeled or unlabeled) start configuration and need to find a schedule of sliding moves to transform it into a desired goal configuration, maintaining connectivity of the configuration at all times. Recent work from Computational Geometry has aimed at minimizing the total number of moves, resulting in schedules that can perform reconfigurations in $\mathcal{O}(n^2)$ moves, or $\mathcal{O}(nP)$ for an arrangement of bounding box perimeter size P, but are fully sequential. Here we provide first results in the sliding square model that exploit parallel robot motion, resulting in an optimal speedup to achieve reconfiguration in worst-case optimal makespan of $\mathcal{O}(P)$. We also provide tight bounds on the complexity of the problem by showing that even deciding the possibility of reconfiguration within makespan 1 is NP-complete in the unlabeled case; for the labeled case, deciding reconfiguration within makespan 2 is NP-complete, while makespan 1 can be decided in polynomial time.

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 is to find a sequence of parallel, collision-free agent motions that minimizes the overall time (the makespan) until all agents have reached their respective targets. A natural case is that of a simply connected polygonal domain with axis-parallel boundaries and integer coordinates, i.e., a simple polyomino, which amounts to a simply connected union of lattice unit squares or cells. We focus on the particularly challenging setting of densely packed agents, i.e., one per cell, which strongly restricts the mobility of agents, and requires intricate coordination of motion. We provide a variety of novel results for this problem, including (1) a characterization of polyominoes in which a reconfiguration plan is guaranteed to exist; (2) a characterization of shape parameters that induce worst-case bounds on the makespan; (3) a suite of algorithms to achieve asymptotically worst-case optimal performance with respect to the achievable stretch for cases with severely limited maneuverability. This corresponds to bounding the ratio between obtained makespan and the lower bound provided by the max-min distance between the start and target position of any agent and our shape parameters. Our results extend findings by Demaine et al. (SIAM Journal on Computing, 2019) who investigated the problem for solid rectangular domains, and in the closely related field of Permutation Routing, as presented by Alpert et al. (Computational Geometry, 2022) for convex pieces of grid graphs.

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.

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 moves. The objective is to reach the new configuration in a minimum amount of time. Problems of this type have been considered before, with recent notable results achieving constant stretch for parallel 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. An important constraint for coordinated reconfiguration is to keep the swarm connected after each time step. In previous work, constant stretch could only be achieved if disconnected reconfiguration is allowed, or for scaled configurations of unlabeled robots; on the other hand, the existence of non-constant lower bounds on the stretch factor was unknown. 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, labeled 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 schedule of makespan 1 exists.

We study the Dispersive Art Gallery Problem with vertex guards: Given a polygon $\mathcal{P}$, with pairwise geodesic Euclidean vertex distance of at least 1, and a rational number $\ell$; decide whether there is a set of vertex guards such that $\mathcal{P}$ is guarded, and the minimum geodesic Euclidean distance between any two guards (the so-called dispersion distance) is at least $\ell$. We show that it is NP-complete to decide whether a polygon with holes has a set of vertex guards with dispersion distance 2. On the other hand, we provide an algorithm that places vertex guards in simple polygons at dispersion distance at least 2. This result is tight, as there are simple polygons in which any vertex guard set has a dispersion distance of at most 2.

We investigate several geometric problems of finding tours and cycle covers with minimum turn cost, which have been studied in the past, with complexity, approximation results, and open problems dating back to work by Arkin et al. in 2001. Many new practical applications have spawned variants: For full coverage, all points have to be covered, for subset coverage, specific points have to be covered, and for penalty coverage, points may be left uncovered by incurring a penalty. We show that finding a minimum-turn (full) cycle cover is NP-hard even in 2-dimensional grid graphs, solving the long-standing open Problem 53 in The Open Problems Project edited by Demaine, Mitchell and O’Rourke. We also prove NP-hardness of finding a subset cycle cover of minimum turn cost in thin grid graphs, for which Arkin et al. gave a polynomial-time algorithm for full coverage; this shows that their boundary techniques cannot be applied to compute exact solutions for subset and penalty variants. We also provide a number of positive results. In particular, we establish the first constant-factor approximation algorithms for all considered subset and penalty problem variants for grid-based instances, based on LP/IP techniques. These geometric versions allow many possible edge directions (and thus, turn angles, such as in hexagonal grids or higher-dimensional variants); our approximation factors improve the combinatorial ones of Arkin et al.

Der globale Wandel stellt mit den einhergehenden außergewöhnlichen Wetterereignissen hohe Anforderungen an das Wassermanagement. In diesem Beitrag stellen wir das Forschungsprojekt EXDIMUM vor, das sich mit Fragestellungen zum Management der Auswirkungen von Extremwetter im Oberharz, insbesondere hinsichtlich Starkregen befasst. Im Projekt wird ein mesoskaliges hydrologisches Einzugsgebietsmo-dell entwickelt, das den Wasserhaushalt abbildet. Mit dessen Hilfe werden Auswirkungen von Landnutzungs-und Klimawandel auf die Hydrologie untersucht. Weiterhin wird ein dynamisches, hochaufgelöstes Abflussmodell dazu dienen, Wasserschutzmaßnahmen bes-ser zu planen. Die Modellierung wird durch ein Sensornetzwerk ergänzt, das Veränderun-gen hydrologischer Größen in Echtzeit erfasst. Der Fernerkundung kommt im Projekt eine wichtige Rolle u.a. bei der Erfassung der Landnutzungsänderungen und insbesondere des Baumsterbens in Folge von Dürreperioden zu. Erste Ergebnisse des noch laufenden Projektes zeigen, dass die Modelle gut die tatsächlichen Verhältnisse abbilden. Einzelne Komponenten konnten bereits beim jüngsten Hochwasser wertvolle Informationen liefern.

We consider the problem of connected coordinated motion planning for a large collective of simple, identical robots: From a given start grid configuration of robots, we need to reach a desired target configuration via a sequence of parallel, collision-free robot motions, such that the set of robots induces a connected grid graph at all integer times. The objective is to minimize the makespan of the motion schedule, i.e., to reach the new configuration in a minimum amount of time. We show that this problem is NP-complete, even for deciding 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. On the algorithmic side, we establish simultaneous constant-factor approximation for two fundamental parameters, by achieving constant stretch for constant scale. Scaled shapes (which arise by increasing all dimensions of a given object by the same multiplicative factor) have been considered in previous seminal work on self-assembly, often with unbounded or logarithmic scale factors; we provide methods for a generalized scale factor, bounded by a constant. Moreover, our algorithm achieves a constant stretch factor: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, then the total duration of our overall schedule is O(d)$\mathcal {O}(d)$, which is optimal up to constant factors.