Dynamics of interactions play an increasingly important role in the analysis of complex networks. A modeling framework to capture this are temporal graphs which consist of a set of vertices (entities in the network) and a set of time-stamped binary interactions between the vertices. We focus on enumerating ∆-cliques, an extension of the concept of cliques to temporal graphs: for a given time period ∆, a ∆-clique in a temporal graph is a set of vertices and a time interval such that all vertices interact with each other at least after every ∆ time steps within the time interval. Viard, Latapy, and Magnien [ASONAM 2015, TCS 2016 proposed a greedy algorithm for enumerating all maximal ∆-cliques in temporal graphs. In contrast to this approach, we adapt the Bron-Kerbosch algorithm-an efficient, recursive backtracking algorithm which enumerates all maximal cliques in static graphs-to the temporal setting. We obtain encouraging results both in theory (concerning worst-case running time analysis based on the parameter "∆-slice degeneracy" of the underlying graph) as well as in practice 1 with experiments on real-world data. The latter culminates in an improvement for most interesting ∆-values concerning running time in comparison with the algorithm of Viard, Latapy, and Magnien.

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We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NPhardness of the introduced matching problem. In particular, we use the matching problem to make partial progress towards answering the open question about the parameterized complexity of Rural Postman with respect to the parameter "number of weakly connected components in the graph induced by the required arcs". This is a more than thirty years open and long-neglected question with significant practical relevance.

An author's profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the H-index. The author is allowed to merge articles; this may affect the H-index. We analyze the (parameterized) computational complexity of maximizing the H-index using article merges. Herein, to model realistic manipulation scenarios, we define a compatibility graph whose edges correspond to plausible merges. Moreover, we consider several different measures for computing the citation count of a merged article. For the measure used by Google Scholar, we give an algorithm that maximizes the H-index in linear time if the compatibility graph has constant-size connected components. In contrast, if we allow to merge arbitrary articles (that is, for compatibility graphs that are cliques), then already increasing the H-index by one is NP-hard. Experiments on Google Scholar profiles of AI researchers show that the H-index can be manipulated substantially only if one merges articles with highly dissimilar titles.

We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP ⊆ coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].

We prove that any polynomial‐time α ( n ) ‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time O ( α ( C ) ) ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where C is the number of weakly connected components in the subgraph induced by the positive‐demand arcs—a small number in many applications. In conjunction with known results, we obtain constant‐factor approximations for C ∈ O ( log n ) and O ( log C / log log C ) ‐approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial‐time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on C and since C = 1 in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262–278 2017

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We propose new practical algorithms to find maximum-cardinality k-plexes in graphs. A k-plex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most k vertices in the k-plex. Cliques are 1-plexes. In analogy to the special case of finding maximum-cardinality cliques, finding maximum-cardinality k-plexes is NP-hard. Complementing previous work, we develop exact combinatorial algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many real-world graphs outperforming the previously used methods.