Henning Fernau

Henning Fernau, Lakshmanan Kuppusamy, Jana Schulz

In this paper, we consider combining the ideas of forbidden random context grammars as well as of ordered grammars with cooperating distributed grammar systems (CDGS). We focus on investigating their generative capacities. Both ideas can be added to CDGS in two ways: either having (e.g.) a strict order of the rules in each component, or having a strict order on the components. This leads to four different scenarios, only some of them have been addressed in the literature before. While in the area of CDGS, many inclusions among language classes have been %are still open questions for decades, the proposed addition of forbidden random context and ordered regulation variants leads to a clear picture which allows us to get down to only five different classes of languages well known from classical regulated rewriting. This way, we also solve some open problems from the literature.

Emmanuel Arrighi, Zhidan Feng, Henning Fernau et al.

The analysis of (social) networks and multi-agent systems is a central theme in Artificial Intelligence. Some line of research deals with finding groups of agents that could work together to achieve a certain goal. To this end, different notions of so-called clusters or communities have been introduced in the literature of graphs and networks. Among these, defensive alliance is a kind of quantitative group structure. However, all studies on the alliance so for have ignored one aspect that is central to the formation of alliances on a very intuitive level, assuming that the agents are preconditioned concerning their attitude towards other agents: they prefer to be in some group (alliance) together with the agents they like, so that they are happy to help each other towards their common aim, possibly then working against the agents outside of their group that they dislike. Signed networks were introduced in the psychology literature to model liking and disliking between agents, generalizing graphs in a natural way. Hence, we propose the novel notion of a defensive alliance in the context of signed networks. We then investigate several natural algorithmic questions related to this notion. These, and also combinatorial findings, connect our notion to that of correlation clustering, which is a well-established idea of finding groups of agents within a signed network. Also, we introduce a new structural parameter for signed graphs, signed neighborhood diversity snd, and exhibit a parameterized algorithm that finds a smallest defensive alliance in a signed graph.

Henning Fernau, Pamela Fleischmann, Kevin Mann et al.

In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of patterns (given by the languages' words) defining the edges in the graph. In particular, we investigate famous languages like the palindromes, copy-words, Lyndon words, and Dyck words to represent all graphs or specific graph classes by restricting these languages.

Emmanuel Arrighi, Henning Fernau, Daniel Lokshtanov et al.

In its most traditional setting, the main concern of optimization theory is the search for optimal solutions for instances of a given computational problem. A recent trend of research in artificial intelligence, called solution diversity, has focused on the development of notions of optimality that may be more appropriate in settings where subjectivity is essential. The idea is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. When combined with techniques from parameterized complexity theory, the paradigm of diversity of solutions offers a powerful algorithmic framework to address problems of practical relevance. In this work, we investigate the impact of this combination in the field of Kemeny Rank Aggregation, a well-studied class of problems lying in the intersection of order theory and social choice theory and also in the field of order theory itself. In particular, we show that the Kemeny Rank Aggregation problem is fixed-parameter tractable with respect to natural parameters providing natural formalizations of the notions of diversity and of the notion of a sufficiently good solution. Our main results work both when considering the traditional setting of aggregation over linearly ordered votes, and in the more general setting where votes are partially ordered.

Petra Wolf, Henning Fernau

The Int_reg-problem of a combinatorial problem P asks, given a nondeterministic automaton M as input, whether the language L(M) accepted by M contains any positive instance of the problem P. We consider the Int_reg-problem for a number of different graph problems and give general criteria that give decision procedures for these Int_reg-problems. To achieve this goal, we consider a natural graph encoding so that the language of all graph encodings is regular. Then, we draw the connection between classical pumping- and interchange-arguments from the field of formal language theory with the graph operations induced on the encoded graph. Our techniques apply among others to the Int_reg-problem of well-known graph problems like Vertex Cover and Independent Set, as well as to subgraph problems, graph-edit problems and graph-partitioning problems, including coloring problems.