133 research outputs found
Algorithmic aspects of disjunctive domination in graphs
For a graph , a set is called a \emph{disjunctive
dominating set} of if for every vertex , is either
adjacent to a vertex of or has at least two vertices in at distance
from it. The cardinality of a minimum disjunctive dominating set of is
called the \emph{disjunctive domination number} of graph , and is denoted by
. The \textsc{Minimum Disjunctive Domination Problem} (MDDP)
is to find a disjunctive dominating set of cardinality .
Given a positive integer and a graph , the \textsc{Disjunctive
Domination Decision Problem} (DDDP) is to decide whether has a disjunctive
dominating set of cardinality at most . In this article, we first propose a
linear time algorithm for MDDP in proper interval graphs. Next we tighten the
NP-completeness of DDDP by showing that it remains NP-complete even in chordal
graphs. We also propose a -approximation
algorithm for MDDP in general graphs and prove that MDDP can not be
approximated within for any unless NP
DTIME. Finally, we show that MDDP is
APX-complete for bipartite graphs with maximum degree
Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm
The minimum-cost flow (MCF) problem is a fundamental optimization problem
with many applications and seems to be well understood. Over the last half
century many algorithms have been developed to solve the MCF problem and these
algorithms have varying worst-case bounds on their running time. However, these
worst-case bounds are not always a good indication of the algorithms'
performance in practice. The Network Simplex (NS) algorithm needs an
exponential number of iterations for some instances, but it is considered the
best algorithm in practice and performs best in experimental studies. On the
other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly
polynomial, but performs badly in experimental studies.
To explain these differences in performance in practice we apply the
framework of smoothed analysis. We show an upper bound of
for the number of iterations of the MMCC algorithm.
Here is the number of nodes, is the number of edges, and is a
parameter limiting the degree to which the edge costs are perturbed. We also
show a lower bound of for the number of iterations of the
MMCC algorithm, which can be strengthened to when
. For the number of iterations of the NS algorithm we show a
smoothed lower bound of .Comment: Extended abstract to appear in the proceedings of COCOON 201
Identically self-blocking clutters
A clutter is identically self-blocking if it is equal to its blocker. We prove that every identically self-blocking clutter different from is nonideal. Our proofs borrow tools from Gauge Duality and Quadratic Programming. Along the way we provide a new lower bound for the packing number of an arbitrary clutter
Minimal Obstructions for Partial Representations of Interval Graphs
Interval graphs are intersection graphs of closed intervals. A generalization
of recognition called partial representation extension was introduced recently.
The input gives an interval graph with a partial representation specifying some
pre-drawn intervals. We ask whether the remaining intervals can be added to
create an extending representation. Two linear-time algorithms are known for
solving this problem.
In this paper, we characterize the minimal obstructions which make partial
representations non-extendible. This generalizes Lekkerkerker and Boland's
characterization of the minimal forbidden induced subgraphs of interval graphs.
Each minimal obstruction consists of a forbidden induced subgraph together with
at most four pre-drawn intervals. A Helly-type result follows: A partial
representation is extendible if and only if every quadruple of pre-drawn
intervals is extendible by itself. Our characterization leads to a linear-time
certifying algorithm for partial representation extension
Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences
We propose algorithms for construction and random generation of hypergraphs
without loops and with prescribed degree and dimension sequences. The objective
is to provide a starting point for as well as an alternative to Markov chain
Monte Carlo approaches. Our algorithms leverage the transposition of properties
and algorithms devised for matrices constituted of zeros and ones with
prescribed row- and column-sums to hypergraphs. The construction algorithm
extends the applicability of Markov chain Monte Carlo approaches when the
initial hypergraph is not provided. The random generation algorithm allows the
development of a self-normalised importance sampling estimator for hypergraph
properties such as the average clustering coefficient.We prove the correctness
of the proposed algorithms. We also prove that the random generation algorithm
generates any hypergraph following the prescribed degree and dimension
sequences with a non-zero probability. We empirically and comparatively
evaluate the effectiveness and efficiency of the random generation algorithm.
Experiments show that the random generation algorithm provides stable and
accurate estimates of average clustering coefficient, and also demonstrates a
better effective sample size in comparison with the Markov chain Monte Carlo
approaches.Comment: 21 pages, 3 figure
Reconfiguration of Cliques in a Graph
We study reconfiguration problems for cliques in a graph, which determine
whether there exists a sequence of cliques that transforms a given clique into
another one in a step-by-step fashion. As one step of a transformation, we
consider three different types of rules, which are defined and studied in
reconfiguration problems for independent sets. We first prove that all the
three rules are equivalent in cliques. We then show that the problems are
PSPACE-complete for perfect graphs, while we give polynomial-time algorithms
for several classes of graphs, such as even-hole-free graphs and cographs. In
particular, the shortest variant, which computes the shortest length of a
desired sequence, can be solved in polynomial time for chordal graphs,
bipartite graphs, planar graphs, and bounded treewidth graphs
On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts
We examine the connections between the classes of cuts in the title. We show that lift-and-project (L&P) cuts from a given disjunction are equivalent to generalized intersection cuts from the family of polyhedra obtained by taking positive combinations of the complements of the inequalities of each term of the disjunction. While L&P cuts from split disjunctions are known to be equivalent to standard intersection cuts (SICs) from the strip obtained by complementing the terms of the split, we show that L&P cuts from more general disjunctions may not be equivalent to any SIC. In particular, we give easily verifiable necessary and sufficient conditions for a L&P cut from a given disjunction D to be equivalent to a SIC from the polyhedral counterpart of D. Irregular L&P cuts, i.e. those that violate these conditions, have interesting properties. For instance, unlike the regular ones, they may cut off part of the corner polyhedron associated with the LP solution from which they are derived. Furthermore, they are not exceptional: their frequency exceeds that of regular cuts. A numerical example illustrates some of the above properties. © 2016 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Societ
Eosinophils Are Important for Protection, Immunoregulation and Pathology during Infection with Nematode Microfilariae
Eosinophil responses typify both allergic and parasitic helminth disease. In helminthic disease, the role of eosinophils can be both protective in immune responses and destructive in pathological responses. To investigate whether eosinophils are involved in both protection and pathology during filarial nematode infection, we explored the role of eosinophils and their granule proteins, eosinophil peroxidase (EPO) and major basic protein-1 (MBP-1), during infection with Brugia malayi microfilariae. Using eosinophil-deficient mice (PHIL), we further clarify the role of eosinophils in clearance of microfilariae during primary, but not challenge infection in vivo. Deletion of EPO or MBP-1 alone was insufficient to abrogate parasite clearance suggesting that either these molecules are redundant or eosinophils act indirectly in parasite clearance via augmentation of other protective responses. Absence of eosinophils increased mast cell recruitment, but not other cell types, into the broncho-alveolar lavage fluid during challenge infection. In addition absence of eosinophils or EPO alone, augmented parasite-induced IgE responses, as measured by ELISA, demonstrating that eosinophils are involved in regulation of IgE. Whole body plethysmography indicated that nematode-induced changes in airway physiology were reduced in challenge infection in the absence of eosinophils and also during primary infection in the absence of EPO alone. However lack of eosinophils or MBP-1 actually increased goblet cell mucus production. We did not find any major differences in cytokine responses in the absence of eosinophils, EPO or MBP-1. These results reveal that eosinophils actively participate in regulation of IgE and goblet cell mucus production via granule secretion during nematode-induced pathology and highlight their importance both as effector cells, as damage-inducing cells and as supervisory cells that shape both innate and adaptive immunity
Degree correlations in directed scale-free networks
Scale-free networks, in which the distribution of the degrees obeys a
power-law, are ubiquitous in the study of complex systems. One basic network
property that relates to the structure of the links found is the degree
assortativity, which is a measure of the correlation between the degrees of the
nodes at the end of the links. Degree correlations are known to affect both the
structure of a network and the dynamics of the processes supported thereon,
including the resilience to damage, the spread of information and epidemics,
and the efficiency of defence mechanisms. Nonetheless, while many studies focus
on undirected scale-free networks, the interactions in real-world systems often
have a directionality. Here, we investigate the dependence of the degree
correlations on the power-law exponents in directed scale-free networks. To
perform our study, we consider the problem of building directed networks with a
prescribed degree distribution, providing a method for proper generation of
power-law-distributed directed degree sequences. Applying this new method, we
perform extensive numerical simulations, generating ensembles of directed
scale-free networks with exponents between~2 and~3, and measuring ensemble
averages of the Pearson correlation coefficients. Our results show that
scale-free networks are on average uncorrelated across directed links for three
of the four possible degree-degree correlations, namely in-degree to in-degree,
in-degree to out-degree, and out-degree to out-degree. However, they exhibit
anticorrelation between the number of outgoing connections and the number of
incoming ones. The findings are consistent with an entropic origin for the
observed disassortativity in biological and technological networks.Comment: 10 pages, 5 figure
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