Given a graph G = (V,E) with a subset S ⊆ E of edges, the edge subset feedback edge set problem is to find a smallest set F of edges such that in G′ = (V,E − F ) no cycle contains an edge in S. We also define a restricted version of this problem, in which no edges in S is allowed to be selected into F to form a solution. In this paper, we give a linear-time algorithm for the edge subset feedbac...

We consider connectivity-augmentation problems in a setting where each potential new edge has a nonnegative cost associated with it, and the task is to achieve a certain connectivity target with at most p new edges of minimum total cost. The main result is that the minimum cost augmentation of edge-connectivity from k − 1 to k with at most p new edges is fixed-parameter tractable parameterized ...

The workflow satisfiability problem (WSP) is a planning problem. Certain sub-classes of this problem have been shown to be fixed-parameter tractable. In this paper we develop an implementation of an algorithm for WSP that has been shown, in our previous paper, to be fixed-parameter for user-independent constraints. In a set of computational experiments, we compare our algorithm to an encoding o...

Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect ...

We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by pathwidth. We generalize bounds for defective coloring to weighted improper coloring and give a bound for weighted improper coloring in terms of the sum of edge w...

Frick and Grohe [J. ACM 48 (2006), 1184–1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we introduce an analogous notion for matroids (locally bounded branch-width) and show the existence of a fixed parameter algorithm for first order logic propertie...

We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable, parameterised by treewidth, whereas List Hamilton Path is W[1]-hard, even parameterised by pathwidth. These results resolve two open questions of Fellows, Fomin, L...

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is [Formula: see text]-hard to decide, by reduction from 3-Dimensional Matching (3DM) and further that the problem is fixed-pa...

We consider the solution of some NP-hard parallel machine scheduling problems involving minimization weighted or unweighted number tardy jobs. first show that these cannot be approximated in polynomial time. Then we propose exponential-time approximation algorithms and fixed parameter tractable exact to solve them.

We show that several problems that are hard for various parameterized complexity classes on general graphs, become fixed parameter tractable on graphs with no small cycles. More specifically, we give fixed parameter algorithms for Dominating Set, t-Vertex Cover (where we need to cover at least t edges) and several of their variants on graphs that have no triangles or cycles of length 4. These p...