20 research outputs found
Equivalence of the filament and overlap graphs of subtrees of limited trees
The overlap graphs of subtrees of a tree are equivalent to subtree filament
graphs, the overlap graphs of subtrees of a star are cocomparability graphs,
and the overlap graphs of subtrees of a caterpillar are interval filament
graphs. In this paper, we show the equivalence of many more classes of subtree
overlap and subtree filament graphs, and equate them to classes of complements
of cochordal-mixed graphs. Our results generalize the previously known results
mentioned above
Weighted Well-Covered Claw-Free Graphs
A graph G is well-covered if all its maximal independent sets are of the same
cardinality. Assume that a weight function w is defined on its vertices. Then G
is w-well-covered if all maximal independent sets are of the same weight. For
every graph G, the set of weight functions w such that G is w-well-covered is a
vector space. Given an input claw-free graph G, we present an O(n^6)algortihm,
whose input is a claw-free graph G, and output is the vector space of weight
functions w, for which G is w-well-covered. A graph G is equimatchable if all
its maximal matchings are of the same cardinality. Assume that a weight
function w is defined on the edges of G. Then G is w-equimatchable if all its
maximal matchings are of the same weight. For every graph G, the set of weight
functions w such that G is w-equimatchable is a vector space. We present an
O(m*n^4 + n^5*log(n)) algorithm which receives an input graph G, and outputs
the vector space of weight functions w such that G is w-equimatchable.Comment: 14 pages, 1 figur
On Minimum Maximal Distance-k Matchings
We study the computational complexity of several problems connected with
finding a maximal distance- matching of minimum cardinality or minimum
weight in a given graph. We introduce the class of -equimatchable graphs
which is an edge analogue of -equipackable graphs. We prove that the
recognition of -equimatchable graphs is co-NP-complete for any fixed . We provide a simple characterization for the class of strongly chordal
graphs with equal -packing and -domination numbers. We also prove that
for any fixed integer the problem of finding a minimum weight
maximal distance- matching and the problem of finding a minimum weight
-independent dominating set cannot be approximated in polynomial
time in chordal graphs within a factor of unless
, where is a fixed constant (thereby
improving the NP-hardness result of Chang for the independent domination case).
Finally, we show the NP-hardness of the minimum maximal induced matching and
independent dominating set problems in large-girth planar graphs.Comment: 15 pages, 4 figure
Efficient domination through eigenvalues
The paper begins with a new characterization of (k, Ļ )-regular sets. Then, using this result as well as the theory of star complements, we derive a simplex-like algorithm for determining whether or not a graph contains a (0, Ļ )-regular set. When Ļ = 1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NPcomplete. If ā1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it doesnāt work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs
Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems
Constraint satisfaction problems (CSPs) are an important formal framework for
the uniform treatment of various prominent AI tasks, e.g., coloring or
scheduling problems. Solving CSPs is, in general, known to be NP-complete and
fixed-parameter intractable when parameterized by their constraint scopes. We
give a characterization of those classes of CSPs for which the problem becomes
fixed-parameter tractable.
Our characterization significantly increases the utility of the CSP framework
by making it possible to decide the fixed-parameter tractability of problems
via their CSP formulations.
We further extend our characterization to the evaluation of unions of
conjunctive queries, a fundamental problem in databases. Furthermore, we
provide some new insight on the frontier of PTIME solvability of CSPs.
In particular, we observe that bounded fractional hypertree width is more
general than bounded hypertree width only for classes that exhibit a certain
type of exponential growth.
The presented work resolves a long-standing open problem and yields powerful
new tools for complexity research in AI and database theory.Comment: Full and extended version of the IJCAI2020 paper with the same titl
A Conceptual Framework for Adapation
This paper presents a white-box conceptual framework for adaptation that promotes a neat separation of the adaptation logic from the application logic through a clear identification of control data and their role in the adaptation logic. The framework provides an original perspective from which we survey archetypal approaches to (self-)adaptation ranging from programming languages and paradigms, to computational models, to engineering solutions