Calendar management tools assist users with coordinating their daily life. Different tasks have to be scheduled according to the user preferences. In many cases, tasks are at different locations and travel times have to be considered. Therefore, these kinds of calendar management problems can be regarded as spatio-temporal optimisation problems and are often variants of traveling salesman probl...

The classical FEEDBACK VERTEX SET problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. FEEDBACK VERTEX SET has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fixed-parameter algorithms have been a rich source of ideas in the field. In this paper we consider...

We show that the DOMINATING SET problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K1,3, the complete bipartite graph on four vertices where the two parts have one and three vertices, respectively) as an induced subgraph. We present an algorithm that uses 2 2)nO(1) time and polynomial space to decide whether a claw-free graph on n v...

Article history: Received 16 June 2011 Received in revised form 1 February 2012 Accepted 11 March 2012 Available online 13 March 2012

We resolve positively a long standing open question regarding the fixed-parameter tractability of the parameterized Directed Feedback Vertex Set problem. In particular, we propose an algorithm which solves this problem in O(8k! ∗ poly(n)).

A fixed-parameter-tractable algorithm, or FPT algorithm for short, gets an instance (I, k) as its input and has to decide whether (I, k) ∈ L for some parameterized problem L. Many parameterized algorithms work in two stages: reduction to a problem kernel and bounded search tree. Their time complexity is then of the form O(p(|I|) + q(k)ξ), where q(k) is the size of the problem kernel. We show ho...

Planning is an important AI task that gives rise to many hard problems. In order to come up with efficient algorithms for this setting, it is important to understand the sources of complexity. For planning problems that are beyond NP, identifying fragments that allow an efficient reduction to SAT can be a feasible approach due to the great performance of modern SAT solvers. In this paper, we us...

The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Unfortunately, the problem is NP-hard. We show that the Kemeny score (and a corresponding Kemeny ranking) of an election can be computed efficiently whenever the average pairwise distance between two input votes is not too large. In other words, Kemeny Score is fixed-parameter tractable with r...