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 1 3 ); for tree-shaped structures, we give an O(N 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.

Abstract-We present a number of powerful local mechanisms for maintaining a dynamic swarm of robots with limited capabilities and information, in the presence of external forces and permanent node failures. We propose a set of local continuous algorithms that together produce a generalization of a Euclidean Steiner tree. At any stage, the resulting overall shape achieves a good compromise between local thickness, global connectivity, and flexibility to further continuous motion of the terminals. The resulting swarm behavior scales well, is robust against node failures, and performs close to the best known approximation bound for a corresponding centralized static optimization problem.

Motivation Disease module mining methods (DMMMs) extract subgraphs that constitute candidate disease mechanisms from molecular interaction networks such as protein-protein interaction (PPI) networks. Irrespective of the employed models, DMMMs typically include non-robust steps in their workflows, i. e., the computed subnetworks vary when running the DMMMs multiple times on equivalent input. This lack of robustness has a negative effect on the trustworthiness of the obtained subnetworks and is hence detrimental for the wide-spread adoption of DMMMs in the biomedical sciences. Results To overcome this problem, we present a new DMMM called ROBUST (robust disease module mining via enumeration of diverse prize-collecting Steiner trees). In a large-scale empirical evaluation, we show that ROBUST outperforms competing methods in terms of robustness, scalability and, in most settings, functional relevance of the produced modules, measured via KEGG gene set enrichment scores and overlap with DisGeNET disease genes. Availability A Python 3 implementation and scripts to reproduce the results reported in this paper are available on GitHub: https://github.com/bionetslab/robust, https://github.com/bionetslab/robust-eval. Supplementary information Supplementary data are available at Bioinformatics online.

No abstract

We investigate a variety of problems of finding tours and cycle covers with minimum turn cost. Questions of this type have been studied in the past, with complexity and approximation results, and open problems dating back to work by Arkin et al. in 2001. A wide spectrum of practical applications have renewed the interest in these questions, and spawned variants: for full coverage, every point has to be covered, for subset coverage, specific points have to be covered, and for penalty coverage, points may be left uncovered by incurring an individual penalty.We make a number of contributions. We first 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 NPhardness 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.On the positive side, we establish the first constant-factor approximation algorithms for all considered subset and penalty problem variants for very general classes of instances, making use of LP/IP techniques. For these generalized graph problems with many possible edge directions (and thus, turn angles, such as in hexagonal grids or higher-dimensional variants), our approximation factors also improve the combinatorial ones of Arkin et al. Our approach can also be extended to other geometric variants, such as scenarios with obstacles and linear combinations of turn and distance costs.