Upper and Lower Bounds for Weak Backdoor Set Detection

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6^k. We also prove a 2^k lower bound for these problems, subject to the Strong Exponential Time Hypothesis.Comment: A short version will appear in the proceedings of the 16th International Conference on Theory and Applications of Satisfiability Testin

A shortcut to (sun)flowers: Kernels in logarithmic space or linear time

We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for preprocessing via simple and/or local reduction rules. We find kernelizations for d-Hitting Set(k), d-Set Packing(k), Edge Dominating Set(k) and a number of hitting and packing problems in graphs, each running in logspace. Additionally, we return to the question of linear-time kernelization. For d-Hitting Set(k) a linear-time kernelization was given by van Bevern [Algorithmica (2014)]. We give a simpler procedure and save a large constant factor in the size bound. Furthermore, we show that we can obtain a linear-time kernel for d-Set Packing(k) as well.Comment: 18 page

Band gap bowing in NixMg1-xO.

Epitaxial transparent oxide NixMg1-xO (0 ≤ x ≤ 1) thin films were grown on MgO(100) substrates by pulsed laser deposition. High-resolution synchrotron X-ray diffraction and high-resolution transmission electron microscopy analysis indicate that the thin films are compositionally and structurally homogeneous, forming a completely miscible solid solution. Nevertheless, the composition dependence of the NixMg1-xO optical band gap shows a strong non-parabolic bowing with a discontinuity at dilute NiO concentrations of x  0.074 and account for the anomalously large band gap narrowing in the NixMg1-xO solid solution system

Evaluation of ILP-based approaches for partitioning into colorful components

The NP-hard Colorful Components problem is a graph partitioning problem on vertex-colored graphs. We identify a new application of Colorful Components in the correction of Wikipedia interlanguage links, and describe and compare three exact and two heuristic approaches. In particular, we devise two ILP formulations, one based on Hitting Set and one based on Clique Partition. Furthermore, we use the recently proposed implicit hitting set framework [Karp, JCSS 2011; Chandrasekaran et al., SODA 2011] to solve Colorful Components. Finally, we study a move-based and a merge-based heuristic for Colorful Components. We can optimally solve Colorful Components for Wikipedia link correction data; while the Clique Partition-based ILP outperforms the other two exact approaches, the implicit hitting set is a simple and competitive alternative. The merge-based heuristic is very accurate and outperforms the move-based one. The above results for Wikipedia data are confirmed by experiments with synthetic instances

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

Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter

An important result in the study of polynomial-time preprocessing shows that there is an algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at most 2k' vertices (and thus O((k')^2) edges) with k' <= k. Using the terminology of parameterized complexity we say that k-Vertex Cover has a kernel with 2k vertices. There is complexity-theoretic evidence that both 2k vertices and Theta(k^2) edges are optimal for the kernel size. In this paper we consider the Vertex Cover problem with a different parameter, the size fvs(G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number vc(G) since fvs(G) <= vc(G) and the difference can be arbitrarily large. We give a kernel for Vertex Cover with a number of vertices that is cubic in fvs(G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that |V(G')| <= 2k and |V(G')| <= O(|X'|^3). A similar result holds when the feedback vertex set X is not given along with the input. In sharp contrast we show that the Weighted Vertex Cover problem does not have a polynomial kernel when parameterized by the cardinality of a given vertex cover of the graph unless NP is in coNP/poly and the polynomial hierarchy collapses to the third level.Comment: Published in "Theory of Computing Systems" as an Open Access publicatio