A randomized polynomial kernel for Subset Feedback Vertex Set

The Subset Feedback Vertex Set problem generalizes the classical Feedback Vertex Set problem and asks, for a given undirected graph $G=(V,E)$, a set $S \subseteq V$, and an integer $k$, whether there exists a set $X$ of at most $k$ vertices such that no cycle in $G-X$ contains a vertex of $S$. It was independently shown by Cygan et al. (ICALP '11, SIDMA '13) and Kawarabayashi and Kobayashi (JCTB '12) that Subset Feedback Vertex Set is fixed-parameter tractable for parameter $k$. Cygan et al. asked whether the problem also admits a polynomial kernelization. We answer the question of Cygan et al. positively by giving a randomized polynomial kernelization for the equivalent version where $S$ is a set of edges. In a first step we show that Edge Subset Feedback Vertex Set has a randomized polynomial kernel parameterized by $|S|+k$ with $O(|S|^2k)$ vertices. For this we use the matroid-based tools of Kratsch and Wahlstr\"om (FOCS '12) that for example were used to obtain a polynomial kernel for $s$-Multiway Cut. Next we present a preprocessing that reduces the given instance $(G,S,k)$ to an equivalent instance $(G',S',k')$ where the size of $S'$ is bounded by $O(k^4)$. These two results lead to a polynomial kernel for Subset Feedback Vertex Set with $O(k^9)$ vertices

Roots and Consequences of Financial Distortions

This thesis links the roots and the consequences excess debt can have for an economy. Chapter 2 studies the impact financial frictions, caused by high debt levels, have on the business cycle. This helps understanding what the consequences of high debt levels are and how they translate to the real economy through business cycle fluctuations. The third chapter stands out as it does not study financial distortions directly but financial intermediation. Nevertheless, it is an important component in the debt and distortions nexus as an enormous share of external finance used by companies is provided by banks. Furthermore, the study sheds light on the question how the banking system is affected by measures introduced in the aftermath of the recent financial crisis, which was caused by financial distortions in the first place. The fourth and last chapter tries to uncover the roots of indebtedness of firms and studies the external finance preferences of European companies. They rely less, in comparison to their American counterparts, on external equity financing and the goal of this chapter is to analyze whether this is rooted in their preferences

Smaller Parameters for Vertex Cover Kernelization

We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{\o}mme [WG 2016] who gave a kernel with $\mathcal{O}(|X|^{12})$ vertices when $X$ is a vertex set such that each connected component of $G-X$ contains at most one cycle, i.e., $X$ is a modulator to a pseudoforest. We strongly generalize this result by using modulators to $d$-quasi-forests, i.e., graphs where each connected component has a feedback vertex set of size at most $d$, and obtain kernels with $\mathcal{O}(|X|^{3d+9})$ vertices. Our result relies on proving that minimal blocking sets in a $d$-quasi-forest have size at most $d+2$. This bound is tight and there is a related lower bound of $\mathcal{O}(|X|^{d+2-\epsilon})$ on the bit size of kernels. In fact, we also get bounds for minimal blocking sets of more general graph classes: For $d$-quasi-bipartite graphs, where each connected component can be made bipartite by deleting at most $d$ vertices, we get the same tight bound of $d+2$ vertices. For graphs whose connected components each have a vertex cover of cost at most $d$ more than the best fractional vertex cover, which we call $d$-quasi-integral, we show that minimal blocking sets have size at most $2d+2$, which is also tight. Combined with existing randomized polynomial kernelizations this leads to randomized polynomial kernelizations for modulators to $d$-quasi-bipartite and $d$-quasi-integral graphs. There are lower bounds of $\mathcal{O}(|X|^{d+2-\epsilon})$ and $\mathcal{O}(|X|^{2d+2-\epsilon})$ for the bit size of such kernels

On Kernelization for Edge Dominating Set under Structural Parameters

In the NP-hard Edge Dominating Set problem (EDS) we are given a graph G=(V,E) and an integer k, and need to determine whether there is a set F subseteq E of at most k edges that are incident with all (other) edges of G. It is known that this problem is fixed-parameter tractable and admits a polynomial kernelization when parameterized by k. A caveat for this parameter is that it needs to be large, i.e., at least equal to half the size of a maximum matching of G, for instances not to be trivially negative. Motivated by this, we study the existence of polynomial kernelizations for EDS when parameterized by structural parameters that may be much smaller than k. Unfortunately, at first glance this looks rather hopeless: Even when parameterized by the deletion distance to a disjoint union of paths P_3 of length two there is no polynomial kernelization (under standard assumptions), ruling out polynomial kernelizations for many smaller parameters like the feedback vertex set size. In contrast, somewhat surprisingly, there is a polynomial kernelization for deletion distance to a disjoint union of paths P_5 of length four. As our main result, we fully classify for all finite sets H of graphs, whether a kernel size polynomial in |X| is possible when given X such that each connected component of G-X is isomorphic to a graph in H

Approximate Turing Kernelization for Problems Parameterized by Treewidth

We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An $\alpha$-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm that, when given access to an oracle that outputs $c$-approximate solutions in $O(1)$ time, obtains an $(\alpha \cdot c)$-approximate solution to the considered problem, using calls to the oracle of size at most $f(k)$ for some function $f$ that only depends on the parameter. Using this definition, we show that Independent Set parameterized by treewidth $\ell$ has a $(1+\varepsilon)$-approximate Turing kernel with $O(\frac{\ell^2}{\varepsilon})$ vertices, answering an open question posed by Lokshtanov et al. [STOC 2017]. Furthermore, we give $(1+\varepsilon)$-approximate Turing kernels for the following graph problems parameterized by treewidth: Vertex Cover, Edge Clique Cover, Edge-Disjoint Triangle Packing and Connected Vertex Cover. We generalize the result for Independent Set and Vertex Cover, by showing that all graph problems that we will call "friendly" admit $(1+\varepsilon)$-approximate Turing kernels of polynomial size when parameterized by treewidth. We use this to obtain approximate Turing kernels for Vertex-Disjoint $H$-packing for connected graphs $H$, Clique Cover, Feedback Vertex Set and Edge Dominating Set

Preprocessing Under Uncertainty: Matroid Intersection

We continue the study of preprocessing under uncertainty that was initiated independently by Assadi et al. (FSTTCS 2015) and Fafianie et al. (STACS 2016). Here, we are given an instance of a tractable problem with a large static/known part and a small part that is dynamic/uncertain, and ask if there is an efficient algorithm that computes an instance of size polynomial in the uncertain part of the input, from which we can extract an optimal solution to the original instance for all (usually exponentially many) instantiations of the uncertain part. In the present work, we focus on the Matroid Intersection problem. Amongst others we present a positive preprocessing result for the important case of finding a largest common independent set in two linear matroids. Motivated by an application for intersecting two gammoids we also revisit Maximum Flow. There we tighten a lower bound of Assadi et al. and give an alternative positive result for the case of low uncertain capacity that yields a Maximum Flow instance as output rather than a matrix

Demokratiska krav på politisk journalistik - med metakommunikation i fokus

Uppsatsen tar en utgångspunkt i Dahls pluralistiska demokratimodells syn på information som centralt i det demokratiska samhället. Politisk PR (spin) problematiseras utifrån detta och en rad krav på journalistiken sätts upp. Metakommunikation, som den presenteras av Frank Esser m.fl., ses som ett bot mot en del av den demokratirelaterade problematik som politisk PR innebär. Innehållsanalys utförs på svenskt pressmaterial för att se om rapporteringen kring organisationen Greenpeace är metakommunicerad

Circuitry rewiring directly couples competence to predation in the gut dweller Streptococcus salivarius

Small distortions in transcriptional networks might lead to drastic phenotypical changes, especially in cellular developmental programs such as competence for natural transformation. Here, we report a pervasive circuitry rewiring for competence and predation interplay in commensal streptococci. Canonically, in streptococci paradigms such as Streptococcus pneumoniae and Streptococcus mutans, the pheromone-based two-component system BlpRH is a central node that orchestrates the production of antimicrobial compounds (bacteriocins) and incorporates signal from the competence activation cascade. However, the human commensal Streptococcus salivarius does not contain a functional BlpRH pair, while the competence signaling system ComRS directly couples bacteriocin production and competence commitment. This network shortcut might underlie an optimal adaptation against microbial competitors and explain the high prevalence of S. salivarius in the human digestive tract. Moreover, the broad spectrum of bacteriocin activity against pathogenic bacteria showcases the commensal and genetically tractable S. salivarius species as a user-friendly model for competence and bacterial predation

Sugar Utilisation and Conservation of the gal-lac Gene Cluster in Streptococcus thermophilus

The adaptation to utilise lactose as primary carbon and energy source is a characteristic for Streptococcus thermophilus. These organisms, however only utilise the glucose moiety of lactose while the galactose moiety is excreted into the growth medium. In this study we evaluated the diversity of sugar utilisation and the conservation of the gal-lac gene cluster in a collection of 18 S. thermophilus strains isolated from a variety of sources. For this purpose analysis was performed on DNA from these isolates and the results were compared with those obtained with a strain from which the complete genome sequence has been determined. The sequence, organisation and flanking regions of the S. thermophilus gal-lac gene cluster were found to be highly conserved among all strains. The vast majority of the S. thermophilus strains were able to utilize only glucose, lactose, and sucrose as carbon sources, some strains could also utilize fructose and two of these were able to grow on galactose. Molecular characterisation of these naturally occurring Gal+ strains revealed up-mutations in the galKTE promoter that were absent in all other strains. These data support the hypothesis that the loss of the ability to ferment galactose can be attributed to the low activity of the galKTE promoter, probably as a consequence of the adaptation to milk in which the lactose levels are in excess