Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time

Given an undirected graph, the task in Cluster Editing is to insert and delete a minimum number of edges to obtain a cluster graph, that is, a disjoint union of cliques. In the weighted variant each vertex pair comes with a weight and the edge modifications have to be of minimum overall weight. In this work, we provide the first polynomial-time algorithm to apply the following data reduction rule of Böcker et al. [Algorithmica, 2011] for Weighted Cluster Editing: For a graph $G = (V,E)$, merge a vertex set $S ⊆ V$ into a single vertex if the minimum cut of G[S] is at least the combined cost of inserting all missing edges within G[S] plus the cost of cutting all edges from S to the rest of the graph. Complementing our theoretical findings, we experimentally demonstrate the effectiveness of the data reduction rule, shrinking real-world test instances from the PACE Challenge 2021 by around 24% while previous heuristic implementations of the data reduction rule only achieve 8%

On the (non-)existence of polynomial kernels for Pl-free edge modification problems

Given a graph G = (V,E) and an integer k, an edge modification problem for a graph property P consists in deciding whether there exists a set of edges F of size at most k such that the graph H = (V,E \vartriangle F) satisfies the property P. In the P edge-completion problem, the set F of edges is constrained to be disjoint from E; in the P edge-deletion problem, F is a subset of E; no constraint is imposed on F in the P edge-edition problem. A number of optimization problems can be expressed in terms of graph modification problems which have been extensively studied in the context of parameterized complexity. When parameterized by the size k of the edge set F, it has been proved that if P is an hereditary property characterized by a finite set of forbidden induced subgraphs, then the three P edge-modification problems are FPT. It was then natural to ask whether these problems also admit a polynomial size kernel. Using recent lower bound techniques, Kratsch and Wahlstrom answered this question negatively. However, the problem remains open on many natural graph classes characterized by forbidden induced subgraphs. Kratsch and Wahlstrom asked whether the result holds when the forbidden subgraphs are paths or cycles and pointed out that the problem is already open in the case of P4-free graphs (i.e. cographs). This paper provides positive and negative results in that line of research. We prove that parameterized cograph edge modification problems have cubic vertex kernels whereas polynomial kernels are unlikely to exist for the Pl-free and Cl-free edge-deletion problems for large enough l

Surface roughness during depositional growth and sublimation of ice crystals

Full version of an earlier discussion paper (Chou et al. 2018)Ice surface properties can modify the scattering properties of atmospheric ice crystals and therefore affect the radiative properties of mixed-phase and cirrus clouds. The Ice Roughness Investigation System (IRIS) is a new laboratory setup designed to investigate the conditions under which roughness develops on single ice crystals, based on their size, morphology and growth conditions (relative humidity and temperature). Ice roughness is quantified through the analysis of speckle in 2-D light-scattering patterns. Characterization of the setup shows that a supersaturation of 20 % with respect to ice and a temperature at the sample position as low as-40 °C could be achieved within IRIS. Investigations of the influence of humidity show that higher supersaturations with respect to ice lead to enhanced roughness and irregularities of ice crystal surfaces. Moreover, relative humidity oscillations lead to gradual ratcheting-up of roughness and irregularities, as the crystals undergo repeated growth-sublimation cycles. This memory effect also appears to result in reduced growth rates in later cycles. Thus, growth history, as well as supersaturation and temperature, influences ice crystal growth and properties, and future atmospheric models may benefit from its inclusion in the cloud evolution process and allow more accurate representation of not just roughness but crystal size too, and possibly also electrification properties.Peer reviewe

Mod/Resc Parsimony Inference

We address in this paper a new computational biology problem that aims at understanding a mechanism that could potentially be used to genetically manipulate natural insect populations infected by inherited, intra-cellular parasitic bacteria. In this problem, that we denote by \textsc{Mod/Resc Parsimony Inference}, we are given a boolean matrix and the goal is to find two other boolean matrices with a minimum number of columns such that an appropriately defined operation on these matrices gives back the input. We show that this is formally equivalent to the \textsc{Bipartite Biclique Edge Cover} problem and derive some complexity results for our problem using this equivalence. We provide a new, fixed-parameter tractability approach for solving both that slightly improves upon a previously published algorithm for the \textsc{Bipartite Biclique Edge Cover}. Finally, we present experimental results where we applied some of our techniques to a real-life data set.Comment: 11 pages, 3 figure

Computing maximum matchings in temporal graphs

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ ∈ ℕ is given. The requirement that a vertex cannot be matched twice in any Δ-window models some necessary "recovery" period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms

Effects of interface morphology and geometry on the thermoelectric properties of artificially structured ZnO-based thin-films

Thermoelectricity may play a major role in waste heat recovery of fossil fuel consuming devices. Unfortunately thermoelectric generators to date only have poor conversion efficiencies (5 %). One way to improve the efficiency is to improve the performance of the active thermoelectric material. For this the figure of merit Z is given by Z=(S^2 sigma)/kappa, where S denotes the Seebeck coefficient, sigma the electrical conductivity, and kappa; the thermal conductivity. Z can be improved by either increasing the numerator S^2 sigma; (the so called power factor) or decreasing the denominator. The typical and best understood thermoelectric materials so far are based on Te, such as Bi2Te3 or PbTe. Unfortunately, for a mass application of thermoelectric devices, estimations show that the tellurium resources will be consumed very quickly. Hence it is worth trying to develop novel thermoelectric materials which are more sustainable and “green”. Exemplarily the thermoelectric properties of ZnO as an ideal model system were investigated in the framework of this thesis. Main goal of the work was to get a better understanding of the influence of effects on the microscopic length scale (e.g. due to thin-films, grain boundaries, artificial structuring) on the macroscopic behavior of the sample. In this context the following results were found: Investigations of degenerately doped thin ZnO:Al films and subsequent annealing in air showed that at very high carrier concentrations, where the samples have metallic character, a sign reversal of S may occur. Although the sample is clearly n-type, small positive Seebeck coefficients can be measured, changing their sign with decreasing temperature. This is due to changes of the density of states at the Fermi-energy in a degenerately doped semiconductor. The energy filtering effect due to grain boundaries, e.g. the increase of the power factor with increasing carrier concentration only works to a certain extend: If the carrier concentration n exceeds a certain value, screening effects diminish the barrier height and width leading to a decrease of the power factor. Concerning the investigation of interfaces first measurements on a multilayer sample series of alternating ZnO/ZnS layers in in-plane geometry gave hints for the formation of interface layers of very high electrical conductivity between ZnO and ZnS, dominating the transport behaviour at large layer thicknesses (d > 100 nm). At smaller d, where d becomes comparable to the typical fluctuation length of the interface roughness, the transport path and hence the thermoelectric properties are strongly determined by the surface fluctuations. These results could be approved qualitatively by simulations within a Network Model (NeMo). Stronger impact on the thermoelectric parameters, especially on the thermal conductivity, were found in cross plane direction, i.e. perpendicular to the interfaces. Unfortunately measurements of multilayers in cross-plane direction are very difficult to perform. To overcome this problem lateral structuring of thin-films offers attractive possibilities. To realize bar structures of alternating materials the method of self-aligned pattern transfer was developed and employed. Measurements perpendicular to the interfaces show that the number of interfaces as well as their shape (i.e. length) and morphology has a strong influence on the power factor. Supported by numerous NeMo simulations the results indicated that the thermoelectric properties across the sample are dominated by the shortest path of electrical conductance. The transport path is strongly influenced by assuming space-charge regions of different width and conductivity. Best agreement between experiment and simulations has been achieved by replacing a certain fraction of the lowly conducting material with a highly conducting space-charge region. However, the origin of this highly conducting surface region requires further clarifications. The findings of this work suggest that due to its high Seebeck coefficients and the possibility to tune the electrical conductivity by doping, ZnO is a promising candidate for an environmentally friendly and sustainable n-type thermoelectric material. The fact that its thermal conductivity is quite high may be overcome by a combination with ZnS. However this back door shown by theory still needs to be approved by experiment.Thermoelektrizität kann eine wichtige Rolle bei der Nutzung der bei der Verbrennung fossiler Rohstoffe entstehenden Abwärme spielen. Leider weisen thermoelektrische Generatoren bisher nur geringe Wirkungsgrade (5%) auf. Eine Möglichkeit, die Effizienz zu verbessern, ist die Leistung des thermoelektrisch aktiven Materials zu verbessern. Kennzahl dafür ist der Gütefaktor Z Z=(S^2 sigma)/kappa, wobei S den Seebeck-Koeffizienten, sigma die elektrische Leitfähigkeit und kappa die thermische Leitfähigkeit bezeichnen. Z kann entweder durch Erhöhen des Zählers S^2 sigma (der sog. Leistungsfaktor) oder Verringern des Nenners verbessert werden. Die zurzeit typischen und am besten verstandenen thermoelektrischen Materialien basieren auf Tellur (Te), wie Bi2Te3 oder PbTe. Für eine breite Anwendung thermoelektrischer Bauteile zeigen allerdings Abschätzungen, dass die Tellurvorkommen schnell aufgebraucht sein werden. Somit macht es Sinn, neue nachhaltige und „grüne“ Materialien zu untersuchen. Beispielhaft wurden dafür innerhalb dieser Arbeit die thermoelektrischen Eigenschaften des idealen Modellsystems ZnO untersucht. Hauptziel dabei war es, die Auswirkungen der Effekte auf mikroskopischer Ebene (z. B. durch Dünnschichten, Korngrenzen, künstliche Strukturierung) auf das makroskopische Verhalten der Probe besser zu verstehen. In diesem Zusammenhang wurden folgende Ergebnisse gefunden: Untersuchungen an entartet dotierten - und anschließend an Luft getemperten ZnO:Al Schichten zeigen, dass bei sehr hohen Ladungsträgerkonzentrationen, bei denen die Proben metallischen Charakter aufweisen, ein Vorzeichenwechsel von S stattfindet. Obwohl die Proben klar n-Typ sind, konnten kleine positive Seebeck-Koeffizienten gemessen werden, die mit abnehmender Temperatur das Vorzeichen wechselten. Dies kann Änderungen in der Zustandsdichte am Ferminiveau dieses entarteten Halbleiters zugeschrieben werden. Der Energie-Filter Effekt bedingt durch Korngrenzen, d. h. das Ansteigen des Leistungsfaktors mit steigender Ladungsträgerkonzentration, konnte nur bis zu einem gewissen Grad beobachtet werden: Falls nämlich die Ladungsträgerkonzentration einen bestimmten Wert übersteigt, verringern sogenannte Abschirmungseffekte die Barrieren Höhe und - Breite, was wiederum zu einer Verkleinerung des Leistungsfaktors führt. Im Hinblick auf die Charakterisierung von Grenzflächen wurden erste Messungen an Übergittern aus alternierenden ZnO/ZnS Schichten in „in-plane“ Geometrie durchgeführt. Die Ergebnisse ließen auf die Ausbildung elektrisch hochleitender Grenzschichten zwischen ZnO und ZnS schließen, welche das Transportverhalten bei hohen Schichtdicken (d > 100 nm) dominieren. Zu geringeren Schichtdicken hin, wo d mit der typischen Oberflächenrauigkeit vergleichbar wird, sind die Transportpfade und damit auch die thermoelektrischen Eigenschaften stark durch Oberflächenfluktuationen bestimmt. Diese Ergebnisse konnten auch qualitativ durch Simulationen innerhalb eines Netzwerkmodells (NeMo) bestätigt werden. Ein stärkerer Einfluss auf die thermoelektrischen Parameter, insbesondere auf die Wärmeleitfähigkeit, wurde in der Literatur in „cross-plane“ Geometrie, d. h. senkrecht zur Grenze, gefunden. Unglücklicherweise sind Messungen an Übergittern in dieser Geometrie sehr schwer durchzuführen. Um dieses Problem zu umgehen bietet die laterale Strukturierung dünner Schichten attraktive Möglichkeiten. Zur Realisierung einer Stegstruktur aus abwechselnden Materialien wurde die Methode der selbstausrichtenden Strukturübertragung im Rahmen dieser Arbeit entwickelt und angewendet. Messungen senkrecht zu den Grenzen zeigen, dass die Anzahl der Grenzen sowie deren Gestalt (d. h. Länge) und Morphologie einen erheblichen Einfluss auf den Leistungsfaktor nehmen. Unterstützt von zahlreichen NeMo Simulationen zeigten die Ergebnisse, dass die thermoelektrischen Eigenschaften über die strukturierte Probe hinweg vom elektrisch kürzesten Transportpfad dominiert werden. Dieser wiederum hängt stark von der Annahme sogenannter Grenzflächenregionen verschiedener Breite und Leitfähigkeit ab. Beste Übereinstimmung zwischen Experiment und Simulationen wurde unter der Annahme erreicht, dass ein bestimmter Teil des schlecht leitenden Materials durch eine hochleitende Grenzflächenregion ersetzt wird. Der Ursprung dieser hochleitenden Region konnte jedoch noch nicht geklärt werden. Die Ergebnisse dieser Arbeit zeigen, dass aufgrund seiner hohen Seebeck-Koeffizienten und der Möglichkeiten durch Dotieren die elektrische Leitfähigkeit einzustellen, ZnO ein geeignetes Materialsystem für umweltfreundliche und nachhaltige thermoelektrische Anwendungen ist. Das Problem, dass es eine hohe Wärmeleitfähigkeit aufweist, könnte durch eine geeignete Kombination mit ZnS gelöst werden. Dieses von der Theorie gezeigte Hintertürchen konnte bislang jedoch noch nicht experimentell bestätigt werden

Computing maximum matchings in temporal graphs.

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ ∈ ℕ is given. The requirement that a vertex cannot be matched twice in any Δ-window models some necessary "recovery" period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms

Heterogeneous ice nucleation: exploring the transition from stochastic to singular freezing behavior

Heterogeneous ice nucleation, a primary pathway for ice formation in the atmosphere, has been described alternately as being stochastic, in direct analogy with homogeneous nucleation, or singular, with ice nuclei initiating freezing at deterministic temperatures. We present an idealized, conceptual model to explore the transition between stochastic and singular ice nucleation. This "soccer ball" model treats particles as being covered with surface sites (patches of finite area) characterized by different nucleation barriers, but with each surface site following the stochastic nature of ice embryo formation. The model provides a phenomenological explanation for seemingly contradictory experimental results obtained in our research groups. Even with ice nucleation treated fundamentally as a stochastic process this process can be masked by the heterogeneity of surface properties, as might be typical for realistic atmospheric particle populations. Full evaluation of the model findings will require experiments with well characterized ice nucleating particles and the ability to vary both temperature and waiting time for freezing