118,119 research outputs found
The Parameterized Complexity of Domination-type Problems and Application to Linear Codes
We study the parameterized complexity of domination-type problems.
(sigma,rho)-domination is a general and unifying framework introduced by Telle:
a set D of vertices of a graph G is (sigma,rho)-dominating if for any v in D,
|N(v)\cap D| in sigma and for any $v\notin D, |N(v)\cap D| in rho. We mainly
show that for any sigma and rho the problem of (sigma,rho)-domination is W[2]
when parameterized by the size of the dominating set. This general statement is
optimal in the sense that several particular instances of
(sigma,rho)-domination are W[2]-complete (e.g. Dominating Set). We also prove
that (sigma,rho)-domination is W[2] for the dual parameterization, i.e. when
parameterized by the size of the dominated set. We extend this result to a
class of domination-type problems which do not fall into the
(sigma,rho)-domination framework, including Connected Dominating Set. We also
consider problems of coding theory which are related to domination-type
problems with parity constraints. In particular, we prove that the problem of
the minimal distance of a linear code over Fq is W[2] for both standard and
dual parameterizations, and W[1]-hard for the dual parameterization.
To prove W[2]-membership of the domination-type problems we extend the
Turing-way to parameterized complexity by introducing a new kind of non
deterministic Turing machine with the ability to perform `blind' transitions,
i.e. transitions which do not depend on the content of the tapes. We prove that
the corresponding problem Short Blind Multi-Tape Non-Deterministic Turing
Machine is W[2]-complete. We believe that this new machine can be used to prove
W[2]-membership of other problems, not necessarily related to dominationComment: 19 pages, 2 figure
On the multipacking number of grid graphs
In 2001, Erwin introduced broadcast domination in graphs. It is a variant of
classical domination where selected vertices may have different domination
powers. The minimum cost of a dominating broadcast in a graph is denoted
. The dual of this problem is called multipacking: a multipacking
is a set of vertices such that for any vertex and any positive integer
, the ball of radius around contains at most vertices of .
The maximum size of a multipacking in a graph is denoted mp(G). Naturally
mp(G) . Earlier results by Farber and by Lubiw show that
broadcast and multipacking numbers are equal for strongly chordal graphs. In
this paper, we show that all large grids (height at least 4 and width at least
7), which are far from being chordal, have their broadcast and multipacking
numbers equal
A theoretical and practical study on linear reforms of dual taxes
We extend the linear reforms introduced by Pf ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act 35/2006) introduced with respect to the previous tax.lattices, dual taxes, lorenz domination, linear reforms
A theoretical and practical study on linear reforms of dual taxes
We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.Dual taxes, linear reforms, Lorenz domination, lattices
Remarks on restrained domination and total restrained domination in graphs
summary:The restrained domination number and the total restrained domination number of a graph were introduced recently by various authors as certain variants of the domination number of . A well-known numerical invariant of a graph is the domatic number which is in a certain way related (and may be called dual) to . The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions
El régimen dual en Israel desde 1967
Este artículo aborda el establecimiento del peculiar régimen de dominación dual de Israel desde 1967, argumentando que la estructura de este régimen convierte a las élites militares en un actor político crucial. El régimen dual se basa en la separación geThis article discusses the establishment of Israel's peculiar dual domination regime since 1967, claiming that the structure of this dual regime makes the military elites a crucial political actor. The dual regime is based on geographic separation betwee
Double domination and total -domination in digraphs and their dual problems
A subset of vertices of a digraph is a double dominating set (total
-dominating set) if every vertex not in is adjacent from at least two
vertices in , and every vertex in is adjacent from at least one vertex
in (the subdigraph induced by has no isolated vertices). The double
domination number (total -domination number) of a digraph is the minimum
cardinality of a double dominating set (total -dominating set) in . In
this work, we investigate these concepts which can be considered as two
extensions of double domination in graphs to digraphs, along with the concepts
-limited packing and total -limited packing which have close
relationships with the above-mentioned concepts
- …