184 research outputs found
Parameterized (in)approximability of subset problems
We discuss approximability and inapproximability in FPT-time for a large
class of subset problems where a feasible solution is a subset of the input
data and the value of is . The class handled encompasses many
well-known graph, set, or satisfiability problems such as Dominating Set,
Vertex Cover, Set Cover, Independent Set, Feedback Vertex Set, etc. In a first
time, we introduce the notion of intersective approximability that generalizes
the one of safe approximability and show strong parameterized inapproximability
results for many of the subset problems handled. Then, we study approximability
of these problems with respect to the dual parameter where is the
size of the instance and the standard parameter. More precisely, we show
that under such a parameterization, many of these problems, while
W[]-hard, admit parameterized approximation schemata.Comment: 7 page
Computing the partition function for graph homomorphisms
We introduce the partition function of edge-colored graph homomorphisms, of
which the usual partition function of graph homomorphisms is a specialization,
and present an efficient algorithm to approximate it in a certain domain.
Corollaries include efficient algorithms for computing weighted sums
approximating the number of k-colorings and the number of independent sets in a
graph, as well as an efficient procedure to distinguish pairs of edge-colored
graphs with many color-preserving homomorphisms G --> H from pairs of graphs
that need to be substantially modified to acquire a color-preserving
homomorphism G --> H.Comment: constants are improved, following a suggestion by B. Buk
Improving bounds on large instances of graph coloring
This thesis explores new methods, using both vertex cover and exact graph coloring algorithms in addition to our implementation of the state of the art, to develop a hybrid algorithm that on most instances is able to tighten the bounds or determine the optimal number of colors outright
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
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