We show that a number of election-related problems with prices (such as, for example, bribery) are fixed-parameter tractable (in FPT) when parameterized by the number of candidates. For bribery, this resolves a nearly 10-year old family of open problems. Our results follow by a general technique that formulates voting problems as covering problems and extends the classic approach of using integ...

We present a simple and effective approach to learning tractable conditional random fields with structure that depends on the evidence. Our approach retains the advantages of tractable discriminative models, namely efficient exact inference and arbitrarily accurate parameter learning in polynomial time. At the same time, our algorithm does not suffer a large expressive power penalty inherent to...

This paper proves that the existence of a feasible schedule for set dependent tasks unit execution times with release dates and deadlines on limited number processors is fixed-parameter tractable problem. The parameter considered pathwidth interval graph associated time windows tasks. A algorithm based dynamic programming approach developed proved to solve this decision Fixed-parameter algorith...

Eulerian Extension (EE) is the problem to make an arcweighted directed multigraph Eulerian by adding arcs of minimum total cost. EE is NP-hard and has been shown fixed-parameter tractable with respect to the number of arc additions. Complementing this result, on the way to answering an open question, we show that EE is fixedparameter tractable with respect to the combined parameter “number of c...

Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range of applications, only few tractable fragments of ILP are known, probably the most prominent of which is based on the notion of total unimodularity. Using ent...

We consider the complexity of the firefighter problem where a budget of b ≥ 1 firefighters are available at each time step. This problem is proved to be NP-complete even on trees of degree at most three and b = 1 [10] and on trees of bounded degree b+3 for any fixed b ≥ 2 [3]. In this paper, we provide further insight into the complexity landscape of the problem by showing a complexity dichotom...

We study the NP-hard problem of finding a directed acyclic graph (DAG) on a given set of nodes so as to maximize a given scoring function. The problem models the task of inferring a probabilistic network from data, which has been studied extensively in the fields of artificial intelligence and machine learning. Several variants of the problem, where the output DAG is constrained in several ways...

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...

The relation of constant-factor approximability to fixed-parameter tractability and kernelization is a long-standing open question. We prove that two large classes of constant-factor approximable problems, namely MIN FΠ1 and MAX NP, including the well-known subclass MAX SNP, admit polynomial kernelizations for their natural decision versions. This extends results of Cai and Chen (JCSS 1997), st...

The problem of packing k edge-disjoint triangles in a graph has been thoroughly studied both in the classical complexity and the approximation fields and it has a wide range of applications in many areas, especially computational biology [BP96]. In this paper we present an analysis of the problem from a parameterized complexity viewpoint. We describe a fixed-parameter tractable algorithm for th...