527 research outputs found
Fast Biclustering by Dual Parameterization
We study two clustering problems, Starforest Editing, the problem of adding and deleting edges to obtain a disjoint union of stars, and the generalization Bicluster Editing. We show that, in addition to being NP-hard, none of the problems can be solved in subexponential time unless the exponential time hypothesis fails.
Misra, Panolan, and Saurabh (MFCS 2013) argue that introducing a bound on the number of connected components in the solution should not make the problem easier: In particular, they argue that the subexponential time algorithm for editing to a fixed number of clusters (p-Cluster Editing) by Fomin et al. (J. Comput. Syst. Sci., 80(7) 2014) is an exception rather than the rule. Here, p is a secondary parameter, bounding the number of components in the solution.
However, upon bounding the number of stars or bicliques in the solution, we obtain algorithms which run in time O(2^{3*sqrt(pk)} + n + m) for p-Starforest Editing and O(2^{O(p * sqrt(k) * log(pk))} + n + m) for p-Bicluster Editing. We obtain a similar result for the more general case of t-Partite p-Cluster Editing. This is subexponential in k for a fixed number of clusters, since p is then considered a constant.
Our results even out the number of multivariate subexponential time algorithms and give reasons to believe that this area warrants further study
A Faster Parameterized Algorithm for Treedepth
The width measure \emph{treedepth}, also known as vertex ranking, centered
coloring and elimination tree height, is a well-established notion which has
recently seen a resurgence of interest. We present an algorithm which---given
as input an -vertex graph, a tree decomposition of the graph of width ,
and an integer ---decides Treedepth, i.e. whether the treedepth of the graph
is at most , in time . If necessary, a witness structure
for the treedepth can be constructed in the same running time. In conjunction
with previous results we provide a simple algorithm and a fast algorithm which
decide treedepth in time and ,
respectively, which do not require a tree decomposition as part of their input.
The former answers an open question posed by Ossona de Mendez and Nesetril as
to whether deciding Treedepth admits an algorithm with a linear running time
(for every fixed ) that does not rely on Courcelle's Theorem or other heavy
machinery. For chordal graphs we can prove a running time of for the same algorithm.Comment: An extended abstract was published in ICALP 2014, Track
Fast Biclustering by Dual Parameterization
We study two clustering problems, Starforest Editing, the problem of adding
and deleting edges to obtain a disjoint union of stars, and the generalization
Bicluster Editing. We show that, in addition to being NP-hard, none of the
problems can be solved in subexponential time unless the exponential time
hypothesis fails.
Misra, Panolan, and Saurabh (MFCS 2013) argue that introducing a bound on the
number of connected components in the solution should not make the problem
easier: In particular, they argue that the subexponential time algorithm for
editing to a fixed number of clusters (p-Cluster Editing) by Fomin et al. (J.
Comput. Syst. Sci., 80(7) 2014) is an exception rather than the rule. Here, p
is a secondary parameter, bounding the number of components in the solution.
However, upon bounding the number of stars or bicliques in the solution, we
obtain algorithms which run in time for p-Starforest
Editing and for p-Bicluster Editing. We
obtain a similar result for the more general case of t-Partite p-Cluster
Editing. This is subexponential in k for fixed number of clusters, since p is
then considered a constant.
Our results even out the number of multivariate subexponential time
algorithms and give reasons to believe that this area warrants further study.Comment: Accepted for presentation at IPEC 201
Lower Bounds on the Complexity of MSO_1 Model-Checking
One of the most important algorithmic meta-theorems is a famous result
by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (MSO2) is decidable in linear time on any class of graphs of bounded tree-width. In the parlance of parameterized complexity, this means that MSO2 model-checking is fixed-parameter tractable with respect to the tree-width as parameter. Recently, Kreutzer and Tazari proved a corresponding complexity lower-bound---that MSO2 model-checking is not even in XP wrt the formula size as parameter for graph classes that are subgraph-closed and whose tree-width is poly-logarithmically unbounded. Of course, this is not an unconditional result but holds modulo a certain complexity-theoretic assumption, namely, the Exponential Time Hypothesis (ETH).
In this paper we present a closely related result. We show that
even MSO1 model-checking with a fixed set of vertex labels,
but without edge-set quantifications, is not in XP wrt the formula
size as parameter for graph classes which are subgraph-closed and
whose tree-width is poly-logarithmically unbounded unless the non-uniform ETH fails. In comparison to Kreutzer and Tazari, (1) we use a stronger prerequisite, namely non-uniform instead of uniform ETH, to avoid the effectiveness assumption and the construction of certain obstructions used in their proofs; and (2) we assume a different set of problems to be efficiently decidable, namely MSO1-definable properties on vertex labeled graphs instead of MSO2-definable properties on unlabeled graphs.
Our result has an interesting consequence in the realm of digraph width measures: Strengthening a recent result, we show that no
subdigraph-monotone measure can be algorithmically useful, unless it is within a poly-logarithmic factor of (undirected) tree-width
Preferential potentiation of the effects of serotonin uptake inhibitors by 5-HT1A receptor antagonists in the dorsal raphe pathway: role of somatodendritic autoreceptors
5-HT1A autoreceptor antagonists enhance the effects of antidepressants by preventing a negative feedback of serotonin (5-HT) at somatodendritic level. The maximal elevations of extracellular concentration of 5-HT (5-HT(ext)) induced by the 5-HT uptake inhibitor paroxetine in forebrain were potentiated by the 5-HT1A antagonist WAY-100635 (1 mg/kg s.c.) in a regionally dependent manner (striatum > frontal cortex > dorsal hippocampus). Paroxetine (3 mg/kg s.c.) decreased forebrain 5-HT(ext) during local blockade of uptake. This reduction was greater in striatum and frontal cortex than in dorsal hippocampus and was counteracted by the local and systemic administration of WAY-100635. The perfusion of 50 micromol/L citalopram in the dorsal or median raphe nucleus reduced 5-HT(ext) in frontal cortex or dorsal hippocampus to 40 and 65% of baseline, respectively. The reduction of cortical 5-HT(ext) induced by perfusion of citalopram in midbrain raphe was fully reversed by WAY-100635 (1 mg/kg s.c.). Together, these data suggest that dorsal raphe neurons projecting to striatum and frontal cortex are more sensitive to self-inhibition mediated by 5-HT1A autoreceptors than median raphe neurons projecting to the hippocampus. Therefore, potentiation by 5-HT1A antagonists occurs preferentially in forebrain areas innervated by serotonergic neurons of the dorsal raphe nucleus.Peer reviewe
Lower Bounds on the Complexity of MSO1 Model-Checking
One of the most important algorithmic meta-theorems is a famous result by
Courcelle, which states that any graph problem definable in monadic
second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is
decidable in linear time on any class of graphs of bounded tree-width.
Recently, Kreutzer and Tazari proved a corresponding complexity lower-bound -
that MSO2 model-checking is not even in XP wrt. the formula size as parameter
for graph classes that are subgraph-closed and whose tree-width is
poly-logarithmically unbounded. Of course, this is not an unconditional result
but holds modulo a certain complexity-theoretic assumption, namely, the
Exponential Time Hypothesis (ETH).
In this paper we present a closely related result. We show that even MSO1
model-checking with a fixed set of vertex labels, but without edge-set
quantifications, is not in XP wrt. the formula size as parameter for graph
classes which are subgraph-closed and whose tree-width is poly-logarithmically
unbounded unless the non-uniform ETH fails. In comparison to Kreutzer and
Tazari; we use a stronger prerequisite, namely non-uniform instead of
uniform ETH, to avoid the effectiveness assumption and the construction of
certain obstructions used in their proofs; and we assume a different set
of problems to be efficiently decidable, namely MSO1-definable properties on
vertex labeled graphs instead of MSO2-definable properties on unlabeled graphs.
Our result has an interesting consequence in the realm of digraph width
measures: Strengthening the recent result, we show that no subdigraph-monotone
measure can be "algorithmically useful", unless it is within a poly-logarithmic
factor of undirected tree-width
On the Directed Full Degree Spanning Tree Problem
Abstract. We study the parameterized complexity of a directed analog of the Full Degree Spanning Tree problem where, given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree T of D such that at least k vertices in T have the same out-degree as in D. We show that this problem is W[1]-hard even on the class of directed acyclic graphs. In the dual version, called Reduced Degree Spanning Tree, one is required to construct a spanning out-tree T such that at most k vertices in T have out-degrees that are different from that in D. We show that this problem is fixed-parameter tractable and that it admits a problem kernel with at most 8k vertices on strongly connected digraphs and O(k 2 ) vertices on general digraphs. We also give an algorithm for this problem on general digraphs with running time O(5.942 k · n O(1) ), where n is the number of vertices in the input digraph
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