Exploiting c\mathbf{c}-Closure in Kernelization Algorithms for Graph Problems

A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number such that G is c-closed. Fox et al. [ICALP '18] defined c-closure and investigated it in the context of clique enumeration. We show that c-closure can be applied in kernelization algorithms for several classic graph problems. We show that Dominating Set admits a kernel of size k^O(c), that Induced Matching admits a kernel with O(c^7*k^8) vertices, and that Irredundant Set admits a kernel with O(c^(5/2)*k^3) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show

Electron-phonon interaction and transport properties of metallic bulk and monolayer transition metal dichalcogenide TaS2_2

Transition metal dichalcogenides have recently emerged as promising two-dimensional materials with intriguing electronic properties. Existing calculations of intrinsic phonon-limited electronic transport so far have concentrated on the semicondcucting members of this family. In this paper we extend these studies by investigating the influence of electron-phonon coupling on the electronic transport properties and band renormalization of prototype inherent metallic bulk and monolayer TaS$_2$. Based on density functional perturbation theory and semi-classical Boltzmann transport calculations, promising room temperature mobilities and sheet conductances are found, which can compete with other established 2D materials, leaving TaS$_2$ as promising material candidate for transparent conductors or as atomically thin interconnects. Throughout the paper, the electronic and transport properties of TaS$_2$ are compared to those of its isoelectronic counterpart TaSe$_2$ and additional informations to the latter are given. We furthermore comment on the conventional su- perconductivity in TaS$_2$, where no phonon-mediated enhancement of TC in the monolayer compared to the bulk state was found.Comment: accepted in IOPscience 2D Materials, supplemental material is available on the publishers pag

Resolvins and inflammatory pain

Resolvins are a group of molecules derived from omega-3 fatty acids. They are part of a biochemical program that allows inflamed tissues to return to homeostasis once the need for the inflammatory response is over. Resolvins act in very low dose ranges in vitro and in vivo. New data suggest that they might have the potential to become very potent analgesic drugs in inflammatory pain

Linking foraging strategies of marine calanoid copepods to patterns of nitrogen stable isotope signatures in a mesocosm study

The foraging modes of calanoid copepods differ in that stationary suspension-feeding is more easily detected by prey with strong escape responses (ciliates) than is ‘cruising’ or ‘ambushing’ feeding. Thus, the ability of a copepod to include heterotrophic prey in its diet may be associated with its foraging mode and, further, with its nitrogen stable isotope signature (δ15N). This is because a more carnivorous diet may be expected to result in a higher δ15N. We tested this hypothesis in a mesocosm study using a density gradient (0 to 80 ind. l-1) of calanoid copepods. We expected copepod δ15N to generally increase with decreasing copepod density because of increased food availability, and predicted stronger increases for cruising than for stationary suspension-feeding species. As an assemblage, copepods had a pronounced impact on the food web: diatoms and ciliates decreased, whereas nanoflagellates increased with increasing copepod density. As expected, Centropages hamatus, a cruising species, showed the strongest isotopic increase and also highest population growth at low copepod density, suggesting that it was the most efficient species in capturing ciliates. Temora longicornis, a stationary suspension-feeder, showed a uniform isotopic increase in all mesocosms, which we believe resulted from nutritional stress arising from poor feeding on both ciliates (too fast for ingestion by T. longicornis) and nanoflagellates (too small). However, Pseudocalanus elongatus, a species equally categorised as a stationary suspension-feeder, showed increases in its δ15N similar to those for C. hamatus. While this may indicate potential switching in its foraging mode, alternative explanations cannot be ruled out, partly because qualitative and quantitative aspects of trophic enrichment in our experiment could not be clearly separated. This study shows that consumer δ15N are difficult to interpret, even if potential food sources and aspects of the species’ biology are known, and thus emphasises the necessity for further laboratory studies to help better interpret zooplankton δ15N in the field

Ethernet - a survey on its fields of application

During the last decades, Ethernet progressively became the most widely used local area networking (LAN) technology. Apart from LAN installations, Ethernet became also attractive for many other fields of application, ranging from industry to avionics, telecommunication, and multimedia. The expanded application of this technology is mainly due to its significant assets like reduced cost, backward-compatibility, flexibility, and expandability. However, this new trend raises some problems concerning the services of the protocol and the requirements for each application. Therefore, specific adaptations prove essential to integrate this communication technology in each field of application. Our primary objective is to show how Ethernet has been enhanced to comply with the specific requirements of several application fields, particularly in transport, embedded and multimedia contexts. The paper first describes the common Ethernet LAN technology and highlights its main features. It reviews the most important specific Ethernet versions with respect to each application field’s requirements. Finally, we compare these different fields of application and we particularly focus on the fundamental concepts and the quality of service capabilities of each proposal

Covering Many (Or Few) Edges with k Vertices in Sparse Graphs

We study the following two fixed-cardinality optimization problems (a maximization and a minimization variant). For a fixed ? between zero and one we are given a graph and two numbers k ? ? and t ? ?. The task is to find a vertex subset S of exactly k vertices that has value at least (resp. at most for minimization) t. Here, the value of a vertex set computes as ? times the number of edges with exactly one endpoint in S plus 1-? times the number of edges with both endpoints in S. These two problems generalize many prominent graph problems, such as Densest k-Subgraph, Sparsest k-Subgraph, Partial Vertex Cover, and Max (k,n-k)-Cut. In this work, we complete the picture of their parameterized complexity on several types of sparse graphs that are described by structural parameters. In particular, we provide kernelization algorithms and kernel lower bounds for these problems. A somewhat surprising consequence of our kernelizations is that Partial Vertex Cover and Max (k,n-k)-Cut not only behave in the same way but that the kernels for both problems can be obtained by the same algorithms

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs

A graph $G$ is weakly $\gamma$-closed if every induced subgraph of $G$ contains one vertex $v$ such that for each non-neighbor $u$ of $v$ it holds that $|N(u)\cap N(v)|<\gamma$. The weak closure $\gamma(G)$ of a graph, recently introduced by Fox et al. [SIAM J. Comp. 2020], is the smallest number such that $G$ is weakly $\gamma$-closed. This graph parameter is never larger than the degeneracy (plus one) and can be significantly smaller. Extending the work of Fox et al. [SIAM J. Comp. 2020] on clique enumeration, we show that several problems related to finding dense subgraphs, such as the enumeration of bicliques and $s$-plexes, are fixed-parameter tractable with respect to $\gamma(G)$. Moreover, we show that the problem of determining whether a weakly $\gamma$-closed graph $G$ has a subgraph on at least $k$ vertices that belongs to a graph class $\mathcal{G}$ which is closed under taking subgraphs admits a kernel with at most $\gamma k^2$ vertices. Finally, we provide fixed-parameter algorithms for Independent Dominating Set and Dominating Clique when parameterized by $\gamma+k$ where $k$ is the solution size.Comment: Appeared in ISAAC '2