Parameterized Approximation Schemes using Graph Widths

Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard to solve exactly when parameterized by treewidth or clique-width. Our main contribution is to present a natural randomized rounding technique that extends well-known ideas and can be used for both of these widths. Applying this very generic technique we obtain approximation schemes for a number of problems, evading both polynomial-time inapproximability and parameterized intractability bounds

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

Influence Diffusion in Social Networks under Time Window Constraints

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network $G=(V,E)$, an integer value $t(v)$ for each node $v\in V$, and a time window size $\lambda$. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node $v$ becomes influenced if the number of its neighbors that have been influenced in the previous $\lambda$ rounds is greater than or equal to $t(v)$. We prove that the problem of finding a minimum cardinality target set that influences the whole network $G$ is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared in: Proceedings of 20th International Colloquium on Structural Information and Communication Complexity (Sirocco 2013), Lectures Notes in Computer Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201

Present state and future perspectives of using pluripotent stem cells in toxicology research

The use of novel drugs and chemicals requires reliable data on their potential toxic effects on humans. Current test systems are mainly based on animals or in vitro–cultured animal-derived cells and do not or not sufficiently mirror the situation in humans. Therefore, in vitro models based on human pluripotent stem cells (hPSCs) have become an attractive alternative. The article summarizes the characteristics of pluripotent stem cells, including embryonic carcinoma and embryonic germ cells, and discusses the potential of pluripotent stem cells for safety pharmacology and toxicology. Special attention is directed to the potential application of embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs) for the assessment of developmental toxicology as well as cardio- and hepatotoxicology. With respect to embryotoxicology, recent achievements of the embryonic stem cell test (EST) are described and current limitations as well as prospects of embryotoxicity studies using pluripotent stem cells are discussed. Furthermore, recent efforts to establish hPSC-based cell models for testing cardio- and hepatotoxicity are presented. In this context, methods for differentiation and selection of cardiac and hepatic cells from hPSCs are summarized, requirements and implications with respect to the use of these cells in safety pharmacology and toxicology are presented, and future challenges and perspectives of using hPSCs are discussed

Treewidth Governs the Complexity of Target Set Selection

AbstractIn this paper we study the Target Set Selection problem proposed by Kempe, Kleinberg, and Tardos; a problem which gives a nice clean combinatorial formulation for many applications arising in economy, sociology, and medicine. Its input is a graph with vertex thresholds, the social network, and the goal is to find a subset of vertices, the target set, that “activates” a pre-specified number of vertices in the graph. Activation of a vertex is defined via a so-called activation process as follows: Initially, all vertices in the target set become active. Then at each step i of the process, each vertex gets activated if the number of its active neighbors at iteration i−1 exceeds its threshold. The activation process is “monotone” in the sense that once a vertex is activated, it remains active for the entire process.Our contribution is as follows: First, we present an algorithm for Target Set Selection running in nO(w) time, for graphs with n vertices and treewidth bounded by w. This algorithm can be adopted to much more general settings, including the case of directed graphs, weighted edges, and weighted vertices. On the other hand, we also show that it is highly unlikely to find an no(w) time algorithm for Target Set Selection, as this would imply a sub-exponential algorithm for all problems in SNP. Together with our upper bound result, this shows that the treewidth parameter determines the complexity of Target Set Selection to a large extent, and should be taken into consideration when tackling this problem in any scenario. In the last part of the paper we also deal with the “non-monotone” variant of Target Set Selection, and show that this problem becomes #P-hard on graphs with edge weights

Parameterized Approximability of Maximizing the Spread of Influence in Networks

Abstract. In this paper, we consider the problem of maximizing the spread of influence through a social network. Here, we are given a graph G = (V, E), a positive integer k and a threshold value thr(v) attached to each vertex v ∈ V. The objective is then to find a subset of k vertices to “activate ” such that the number of activated vertices at the end of a propagation process is maximum. A vertex v gets activated if at least thr(v) of its neighbors are. We show that this problem is strongly inapproximable in fpt-time with respect to (w.r.t.) parameter k even for very restrictive thresholds. For unanimity thresholds, we prove that the problem is inapproximable in polynomial time and the decision version is W[1]-hard w.r.t. parameter k. On the positive side, it becomes r(n)approximable in fpt-time w.r.t. parameter k for any strictly increasing function r. Moreover, we give an fpt-time algorithm to solve the decision version for bounded degree graphs.

Latency-Bounded Target Set Selection in Social Networks

We study variants of the Target Set Selection problem, first proposed by Kempe et al. In our scenario one is given a graph G = (V,E), integer values t(v) for each vertex v, and the objective is to determine a small set of vertices (target set) that activates a given number (or a given subset) of vertices of G within a prescribed number of rounds. The activation process in G proceeds as follows: initially, at round 0, all vertices in the target set are activated; subsequently at each round r ≥ 1 every vertex of G becomes activated if at least t(v) of its neighbors are active by round r − 1. It is known that the problem of finding a minimum cardinality Target Set that eventually activates the whole graph G is hard to approximate to a factor better than O(2log1−ϵ∣∣V∣∣) . In this paper we give exact polynomial time algorithms to find minimum cardinality Target Sets in graphs of bounded clique-width, and exact linear time algorithms for trees

Latency-bounded target set selection in social networks

Motivated by applications in sociology, economy and medicine, we study variants of the Target Set Selection problem, first proposed by Kempe, Kleinberg and Tardos. In our scenario one is given a graph G=(V,E), integer values t(v) for each vertex v (thresholds ), and the objective is to determine a small set of vertices (target set ) that activates a given number (or a given subset) of vertices of G within a prescribed number of rounds. The activation process in G proceeds as follows: initially, at round 0, all vertices in the target set are activated; subsequently at each round r⩾1 every vertex of G becomes activated if at least t(v) of its neighbors are already active by round r−1. It is known that the problem of finding a minimum cardinality Target Set that eventually activates the whole graph G is hard to approximate to a factor better than O(2log1−ϵ|V|). In this paper we give exact polynomial time algorithms to find minimum cardinality Target Sets in graphs of bounded clique-width, and exact linear time algorithms for trees

On Tractable Cases of Target Set Selection

We study the NP-complete TARGET SET SELECTION (TSS) problem occurring in social network analysis. Complementing results on its approximability and extending results for its restriction to trees and bounded treewidth graphs, we classify the influence of the parameters “diameter”, “cluster edge deletion number”, “vertex cover number”, and “feedback edge set number ” of the underlying graph on the problem’s complexity, revealing both tractable and intractable cases. For instance, even for diameter-two split graphs TSS remains very hard. TSS can be efficiently solved on graphs with small feedback edge set number and also turns out to be fixed-parameter tractable when parameterized by the vertex cover number, both results contrasting known parameterized intractability results for the parameter treewidth. While these tractability results are relevant for sparse networks, we also show efficient fixed-parameter algorithms for the parameter cluster edge deletion number, yielding tractability for certain dense networks