39,454 research outputs found
The set of parameterized k-covers problem
AbstractThe problem of the set of k-covers is a distance measure for strings. Another well-studied string comparison measure is that of parameterized matching. We consider the problem of the set of parameterized k-covers (k-SPC) which combines k-cover measure with parameterized matching. We prove that k-SPC is NP-complete. We describe an approach to solve k-SPC. This approach is based on constructing a logical model for k-SPC
The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation
We study the computational complexity of problems that arise in abstract
argumentation in the context of dynamic argumentation, minimal change, and
aggregation. In particular, we consider the following problems where always an
argumentation framework F and a small positive integer k are given.
- The Repair problem asks whether a given set of arguments can be modified
into an extension by at most k elementary changes (i.e., the extension is of
distance k from the given set).
- The Adjust problem asks whether a given extension can be modified by at
most k elementary changes into an extension that contains a specified argument.
- The Center problem asks whether, given two extensions of distance k,
whether there is a "center" extension that is a distance at most (k-1) from
both given extensions.
We study these problems in the framework of parameterized complexity, and
take the distance k as the parameter. Our results covers several different
semantics, including admissible, complete, preferred, semi-stable and stable
semantics
A practical fpt algorithm for Flow Decomposition and transcript assembly
The Flow Decomposition problem, which asks for the smallest set of weighted
paths that "covers" a flow on a DAG, has recently been used as an important
computational step in transcript assembly. We prove the problem is in FPT when
parameterized by the number of paths by giving a practical linear fpt
algorithm. Further, we implement and engineer a Flow Decomposition solver based
on this algorithm, and evaluate its performance on RNA-sequence data.
Crucially, our solver finds exact solutions while achieving runtimes
competitive with a state-of-the-art heuristic. Finally, we contextualize our
design choices with two hardness results related to preprocessing and weight
recovery. Specifically, -Flow Decomposition does not admit polynomial
kernels under standard complexity assumptions, and the related problem of
assigning (known) weights to a given set of paths is NP-hard.Comment: Introduces software package Toboggan: Version 1.0.
http://dx.doi.org/10.5281/zenodo.82163
Covering Pairs in Directed Acyclic Graphs
The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a
classical problem that provides a clear and simple mathematical formulation for
several applications in different areas and that has an efficient algorithmic
solution. In this paper, we study the computational complexity of two
constrained variants of Minimum Path Cover motivated by the recent introduction
of next-generation sequencing technologies in bioinformatics. The first problem
(MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum
cardinality set of paths "covering" all the vertices such that both vertices of
each pair belong to the same path. For this problem, we show that, while it is
NP-hard to compute if there exists a solution consisting of at most three
paths, it is possible to decide in polynomial time whether a solution
consisting of at most two paths exists. The second problem (MaxRPSP), given a
DAG and a set of pairs of vertices, asks for a path containing the maximum
number of the given pairs of vertices. We show its NP-hardness and also its
W[1]-hardness when parametrized by the number of covered pairs. On the positive
side, we give a fixed-parameter algorithm when the parameter is the maximum
overlapping degree, a natural parameter in the bioinformatics applications of
the problem
Paradigms for Parameterized Enumeration
The aim of the paper is to examine the computational complexity and
algorithmics of enumeration, the task to output all solutions of a given
problem, from the point of view of parameterized complexity. First we define
formally different notions of efficient enumeration in the context of
parameterized complexity. Second we show how different algorithmic paradigms
can be used in order to get parameter-efficient enumeration algorithms in a
number of examples. These paradigms use well-known principles from the design
of parameterized decision as well as enumeration techniques, like for instance
kernelization and self-reducibility. The concept of kernelization, in
particular, leads to a characterization of fixed-parameter tractable
enumeration problems.Comment: Accepted for MFCS 2013; long version of the pape
Model-Checking Problems as a Basis for Parameterized Intractability
Most parameterized complexity classes are defined in terms of a parameterized
version of the Boolean satisfiability problem (the so-called weighted
satisfiability problem). For example, Downey and Fellow's W-hierarchy is of
this form. But there are also classes, for example, the A-hierarchy, that are
more naturally characterised in terms of model-checking problems for certain
fragments of first-order logic.
Downey, Fellows, and Regan were the first to establish a connection between
the two formalisms by giving a characterisation of the W-hierarchy in terms of
first-order model-checking problems. We improve their result and then prove a
similar correspondence between weighted satisfiability and model-checking
problems for the A-hierarchy and the W^*-hierarchy. Thus we obtain very uniform
characterisations of many of the most important parameterized complexity
classes in both formalisms.
Our results can be used to give new, simple proofs of some of the core
results of structural parameterized complexity theory.Comment: Changes in since v2: Metadata update
On Covering Segments with Unit Intervals
We study the problem of covering a set of segments on a line with the minimum number of unit-length intervals, where an interval covers a segment if at least one of the two endpoints of the segment falls in the unit interval. We also study several variants of this problem.
We show that the restrictions of the aforementioned problems to the set of instances in which all the segments have the same length are NP-hard. This result implies several NP-hardness results in the literature for variants and generalizations of the problems under consideration.
We then study the parameterized complexity of the aforementioned problems. We provide tight results for most of them by showing that they are fixed-parameter tractable for the restrictions in which all the segments have the same length, and are W[1]-complete otherwise
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