4,330 research outputs found
Playing with parameters: structural parameterization in graphs
When considering a graph problem from a parameterized point of view, the
parameter chosen is often the size of an optimal solution of this problem (the
"standard" parameter). A natural subject for investigation is what happens when
we parameterize such a problem by various other parameters, some of which may
be the values of optimal solutions to different problems. Such research is
known as parameterized ecology. In this paper, we investigate seven natural
vertex problems, along with their respective parameters: the size of a maximum
independent set, the size of a minimum vertex cover, the size of a maximum
clique, the chromatic number, the size of a minimum dominating set, the size of
a minimum independent dominating set and the size of a minimum feedback vertex
set. We study the parameterized complexity of each of these problems with
respect to the standard parameter of the others.Comment: 17 page
On Coloring Resilient Graphs
We introduce a new notion of resilience for constraint satisfaction problems,
with the goal of more precisely determining the boundary between NP-hardness
and the existence of efficient algorithms for resilient instances. In
particular, we study -resiliently -colorable graphs, which are those
-colorable graphs that remain -colorable even after the addition of any
new edges. We prove lower bounds on the NP-hardness of coloring resiliently
colorable graphs, and provide an algorithm that colors sufficiently resilient
graphs. We also analyze the corresponding notion of resilience for -SAT.
This notion of resilience suggests an array of open questions for graph
coloring and other combinatorial problems.Comment: Appearing in MFCS 201
Hybrid tractability of soft constraint problems
The constraint satisfaction problem (CSP) is a central generic problem in
computer science and artificial intelligence: it provides a common framework
for many theoretical problems as well as for many real-life applications. Soft
constraint problems are a generalisation of the CSP which allow the user to
model optimisation problems. Considerable effort has been made in identifying
properties which ensure tractability in such problems. In this work, we
initiate the study of hybrid tractability of soft constraint problems; that is,
properties which guarantee tractability of the given soft constraint problem,
but which do not depend only on the underlying structure of the instance (such
as being tree-structured) or only on the types of soft constraints in the
instance (such as submodularity). We present several novel hybrid classes of
soft constraint problems, which include a machine scheduling problem,
constraint problems of arbitrary arities with no overlapping nogoods, and the
SoftAllDiff constraint with arbitrary unary soft constraints. An important tool
in our investigation will be the notion of forbidden substructures.Comment: A full version of a CP'10 paper, 26 page
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