721 research outputs found
Efficient Algorithms for Node Disjoint Subgraph Homeomorphism Determination
Recently, great efforts have been dedicated to researches on the management
of large scale graph based data such as WWW, social networks, biological
networks. In the study of graph based data management, node disjoint subgraph
homeomorphism relation between graphs is more suitable than (sub)graph
isomorphism in many cases, especially in those cases that node skipping and
node mismatching are allowed. However, no efficient node disjoint subgraph
homeomorphism determination (ndSHD) algorithms have been available. In this
paper, we propose two computationally efficient ndSHD algorithms based on state
spaces searching with backtracking, which employ many heuristics to prune the
search spaces. Experimental results on synthetic data sets show that the
proposed algorithms are efficient, require relative little time in most of the
testing cases, can scale to large or dense graphs, and can accommodate to more
complex fuzzy matching cases.Comment: 15 pages, 11 figures, submitted to DASFAA 200
Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
The Nielsen-Thurston theory of surface diffeomorphisms shows that useful
dynamical information can be obtained about a surface diffeomorphism from a
finite collection of periodic orbits.In this paper, we extend these results to
homoclinic and heteroclinic orbits of saddle points. These orbits are most
readily computed and studied as intersections of unstable and stable manifolds
comprising homoclinic or heteroclinic tangles in the surface. We show how to
compute a map of a one-dimensional space similar to a train-track which
represents the isotopy-stable dynamics of the surface diffeomorphism relative
to a tangle. All orbits of this one-dimensional representative are globally
shadowed by orbits of the surface diffeomorphism, and periodic, homoclinic and
heteroclinic orbits of the one-dimensional representative are shadowed by
similar orbits in the surface.By constructing suitable surface diffeomorphisms,
we prove that these results are optimal in the sense that the topological
entropy of the one-dimensional representative is the greatest lower bound for
the entropies of diffeomorphisms in the isotopy class.Comment: Version submitted to "Dynamical Systems: An International Journal"
Section 7 has been further revised; the method for pA maps is new. Notation
has been standardised throughou
Exact Localisations of Feedback Sets
The feedback arc (vertex) set problem, shortened FASP (FVSP), is to transform
a given multi digraph into an acyclic graph by deleting as few arcs
(vertices) as possible. Due to the results of Richard M. Karp in 1972 it is one
of the classic NP-complete problems. An important contribution of this paper is
that the subgraphs , of all elementary
cycles or simple cycles running through some arc , can be computed in
and , respectively. We use
this fact and introduce the notion of the essential minor and isolated cycles,
which yield a priori problem size reductions and in the special case of so
called resolvable graphs an exact solution in . We show
that weighted versions of the FASP and FVSP possess a Bellman decomposition,
which yields exact solutions using a dynamic programming technique in times
and
, where , , respectively. The parameters can
be computed in , ,
respectively and denote the maximal dimension of the cycle space of all
appearing meta graphs, decoding the intersection behavior of the cycles.
Consequently, equal zero if all meta graphs are trees. Moreover, we
deliver several heuristics and discuss how to control their variation from the
optimum. Summarizing, the presented results allow us to suggest a strategy for
an implementation of a fast and accurate FASP/FVSP-SOLVER
Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm
Sharkovskii proved that the existence of a periodic orbit in a
one-dimensional dynamical system implies existence of infinitely many periodic
orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of
shear homeomorphisms of the torus. This is done by obtaining a dynamical order
relation on the set of simple orbits and simple pairs. We then use this order
relation for a global analysis for a quantum chaotic physical system called the
kicked accelerated particle.Comment: 31 pages, 24 figures, to appear in Topological Methods in Nonlinear
Analysi
Quantifying the Extent of Lateral Gene Transfer Required to Avert a `Genome of Eden'
The complex pattern of presence and absence of many genes across different
species provides tantalising clues as to how genes evolved through the
processes of gene genesis, gene loss and lateral gene transfer (LGT). The
extent of LGT, particularly in prokaryotes, and its implications for creating a
`network of life' rather than a `tree of life' is controversial. In this paper,
we formally model the problem of quantifying LGT, and provide exact
mathematical bounds, and new computational results. In particular, we
investigate the computational complexity of quantifying the extent of LGT under
the simple models of gene genesis, loss and transfer on which a recent
heuristic analysis of biological data relied. Our approach takes advantage of a
relationship between LGT optimization and graph-theoretical concepts such as
tree width and network flow
Simple realizability of complete abstract topological graphs simplified
An abstract topological graph (briefly an AT-graph) is a pair
where is a graph and is a set of pairs of its edges. The AT-graph is simply
realizable if can be drawn in the plane so that each pair of edges from
crosses exactly once and no other pair crosses. We show that
simply realizable complete AT-graphs are characterized by a finite set of
forbidden AT-subgraphs, each with at most six vertices. This implies a
straightforward polynomial algorithm for testing simple realizability of
complete AT-graphs, which simplifies a previous algorithm by the author. We
also show an analogous result for independent -realizability,
where only the parity of the number of crossings for each pair of independent
edges is specified.Comment: 26 pages, 17 figures; major revision; original Section 5 removed and
will be included in another pape
On retracts, absolute retracts, and folds in cographs
Let G and H be two cographs. We show that the problem to determine whether H
is a retract of G is NP-complete. We show that this problem is fixed-parameter
tractable when parameterized by the size of H. When restricted to the class of
threshold graphs or to the class of trivially perfect graphs, the problem
becomes tractable in polynomial time. The problem is also soluble when one
cograph is given as an induced subgraph of the other. We characterize absolute
retracts of cographs.Comment: 15 page
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