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The parameterized complexity of a problem is generally considered “settled” once it has been shown to be fixed-parameter tractable or to be complete for a class in a parameterized hierarchy such as the weft hierarchy. Several natural parameterized problems have, however, resisted such a classification. In the present paper we argue that, in some cases, this(More)
Bodlaender's Theorem states that for every k there is a linear-time algorithm that decides whether an input graph has tree width k and, if so, computes a width-k tree composition. Cour-celle's Theorem builds on Bodlaender's Theorem and states that for every monadic second-order formula φ and for every k there is a linear-time algorithm that decides whether(More)
Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signaling-regulatory pathways in protein networks. Given a graph and a list of ordered source-target ver-tex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed source-to-target path.(More)
Parameterized complexity theory measures the complexity of computational problems predominantly in terms of their parameterized time complexity. The purpose of the present paper is to demonstrate that the study of parameterized space complexity can give new insights into the complexity of well-studied parameterized problems like the feedback vertex set(More)
An algorithmic meta theorem for a logic and a class C of structures states that all problems ex-pressible in this logic can be solved efficiently for inputs from C. The prime example is Courcelle's Theorem, which states that monadic second-order (mso) definable problems are linear-time solv-able on graphs of bounded tree width. We contribute new algorithmic(More)
String-based negative selection is an immune-inspired classification scheme: Given a self-set S of strings, generate a set D of detectors that do not match any element of S. Then, use these detectors to partition a monitor set M into self and non-self elements. Implementations of this scheme are often impractical because they need exponential time in the(More)
We study on which classes of graphs first-order logic (<scp>fo</scp>) and monadic second-order logic (<scp>mso</scp>) have the same expressive power. We show that for all classes C of graphs that are closed under taking subgraphs, <scp>fo</scp> and <scp>mso</scp> have the same expressive power on C if and only if, C has bounded tree depth. Tree depth is a(More)
We study the expressive power and succinctness of order-invariant sentences of first-order (FO) and monadic second-order (MSO) logic on graphs of bounded tree-depth. Order-invariance is undecidable in general and, therefore, in finite model theory, one strives for logics with a decidable syntax that have the same expressive power as order-invariant(More)