274 research outputs found
Parameterized Inapproximability of Target Set Selection and Generalizations
In this paper, we consider the Target Set Selection problem: given a graph
and a threshold value for any vertex of the graph, find a minimum
size vertex-subset to "activate" s.t. all the vertices of the graph are
activated at the end of the propagation process. A vertex is activated
during the propagation process if at least of its neighbors are
activated. This problem models several practical issues like faults in
distributed networks or word-to-mouth recommendations in social networks. We
show that for any functions and this problem cannot be approximated
within a factor of in time, unless FPT = W[P],
even for restricted thresholds (namely constant and majority thresholds). We
also study the cardinality constraint maximization and minimization versions of
the problem for which we prove similar hardness results
Augmenting graphs to minimize the diameter
We study the problem of augmenting a weighted graph by inserting edges of
bounded total cost while minimizing the diameter of the augmented graph. Our
main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure
Subset feedback vertex set is fixed parameter tractable
The classical Feedback Vertex Set problem asks, for a given undirected graph
G and an integer k, to find a set of at most k vertices that hits all the
cycles in the graph G. Feedback Vertex Set has attracted a large amount of
research in the parameterized setting, and subsequent kernelization and
fixed-parameter algorithms have been a rich source of ideas in the field.
In this paper we consider a more general and difficult version of the
problem, named Subset Feedback Vertex Set (SUBSET-FVS in short) where an
instance comes additionally with a set S ? V of vertices, and we ask for a set
of at most k vertices that hits all simple cycles passing through S. Because of
its applications in circuit testing and genetic linkage analysis SUBSET-FVS was
studied from the approximation algorithms perspective by Even et al.
[SICOMP'00, SIDMA'00].
The question whether the SUBSET-FVS problem is fixed-parameter tractable was
posed independently by Kawarabayashi and Saurabh in 2009. We answer this
question affirmatively. We begin by showing that this problem is
fixed-parameter tractable when parametrized by |S|. Next we present an
algorithm which reduces the given instance to 2^k n^O(1) instances with the
size of S bounded by O(k^3), using kernelization techniques such as the
2-Expansion Lemma, Menger's theorem and Gallai's theorem. These two facts allow
us to give a 2^O(k log k) n^O(1) time algorithm solving the Subset Feedback
Vertex Set problem, proving that it is indeed fixed-parameter tractable.Comment: full version of a paper presented at ICALP'1
Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions
We study the effects of frozen boundaries in a Monte Carlo simulation near a
first order phase transition. Recent theoretical analysis of the dynamics of
first order phase transitions has enabled to state the scaling laws governing
the critical regime of the transition. We check these new scaling laws
performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In
particular, our results support a pseudo-critical beta finite-size scaling of
the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d +
d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not
coincide with the latent heat analytically derived for the same model if
periodic boundary conditions are assumed, which is 0.486358...Comment: 10 pages, 3 postscript figure
Understanding How Inequality in the Distribution of Income Affects Health
Research on the determinants of health has almost exclusively focused on the individual but it seems clear we cannot understand or improve patterns of population health without engaging structural determinants at the societal level. This article traces the development of research on income distribution and health to the most recent epidemiologic studies from the USA that show how income inequality is related to age-adjusted mortality within the 50 States. (r 520.62, p 5 0.0001) even after accounting for absolute levels of income. We discuss potential material, psychological, social and behavioral pathways through which income distribution might be linked to health status. Distributional aspects of the economy are important determinants of health and may well provide one of the most pertinent indicators of overall social well-being.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66686/2/10.1177_135910539700200303.pd
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