481 research outputs found
Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time
We present faster algorithms for computing the 2-edge and 2-vertex strongly
connected components of a directed graph, which are straightforward
generalizations of strongly connected components. While in undirected graphs
the 2-edge and 2-vertex connected components can be found in linear time, in
directed graphs only rather simple -time algorithms were known. We use
a hierarchical sparsification technique to obtain algorithms that run in time
. For 2-edge strongly connected components our algorithm gives the
first running time improvement in 20 years. Additionally we present an -time algorithm for 2-edge strongly connected components, and thus
improve over the running time also when . Our approach
extends to k-edge and k-vertex strongly connected components for any constant k
with a running time of for edges and for vertices
Complexity of Coloring Graphs without Paths and Cycles
Let and denote a path on vertices and a cycle on
vertices, respectively. In this paper we study the -coloring problem for
-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada,
have proved that 3-colorability of -free graphs has a finite forbidden
induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and
Vatshelle have shown that -colorability of -free graphs for
does not. These authors have also shown, aided by a computer search, that
4-colorability of -free graphs does have a finite forbidden induced
subgraph characterization. We prove that for any , the -colorability of
-free graphs has a finite forbidden induced subgraph
characterization. We provide the full lists of forbidden induced subgraphs for
and . As an application, we obtain certifying polynomial time
algorithms for 3-coloring and 4-coloring -free graphs. (Polynomial
time algorithms have been previously obtained by Golovach, Paulusma, and Song,
but those algorithms are not certifying); To complement these results we show
that in most other cases the -coloring problem for -free
graphs is NP-complete. Specifically, for we show that -coloring is
NP-complete for -free graphs when and ; for we show that -coloring is NP-complete for -free graphs
when , ; and additionally, for , we show that
-coloring is also NP-complete for -free graphs if and
. This is the first systematic study of the complexity of the
-coloring problem for -free graphs. We almost completely
classify the complexity for the cases when , and
identify the last three open cases
Target oriented relational model finding
Lecture Notes in Computer Science 8411, 2014Model finders are becoming useful in many software engineering problems. Kodkod is one of the most popular, due to its support for relational logic (a combination of first order logic with relational algebra operators and transitive closure), allowing a simpler specification of constraints, and support for partial instances, allowing the specification of a priori (exact, but potentially partial) knowledge about a problem's solution. However, in some software engineering problems, such as model repair or bidirectional model transformation, knowledge about the solution is not exact, but instead there is a known target that the solution should approximate. In this paper we extend Kodkod's partial instances to allow the specification of such targets, and show how its model finding procedure can be adapted to support them (using both PMax-SAT solvers or SAT solvers with cardinality constraints). Two case studies are also presented, including a careful performance evaluation to assess the effectiveness of the proposed extension.(undefined
Inference of Well-Typings for Logic Programs with Application to Termination Analysis
This paper develops a method to infer a polymorphic well-typing for a logic program. One of the main motivations is to contribute to a better automation of termination analysis in logic programs, by deriving types from which norms can automatically be constructed. Previous work on type-based termination analysis used either types declared by the user, or automatically generated monomorphic types describing the success set of predicates. Declared types are typically more precise and result in stronger termination conditions than those obtained with inferred types. Our type inference procedure involves solving set constraints generated from the program and derives a well-typing in contrast to a success-set approximation. Experiments show that our automatically inferred well-typings are close to the declared types and thus result in termination conditions that are as good as those obtained with declared types for all our experiments to date. We describe the method, its implementation and experiments with termination analysis based on the inferred types
Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition
In the stability analysis of large-scale interconnected systems it is
frequently desirable to be able to determine a decay point of the gain
operator, i.e., a point whose image under the monotone operator is strictly
smaller than the point itself. The set of such decay points plays a crucial
role in checking, in a semi-global fashion, the local input-to-state stability
of an interconnected system and in the numerical construction of a LISS
Lyapunov function. We provide a homotopy algorithm that computes a decay point
of a monotone op- erator. For this purpose we use a fixed point algorithm and
provide a function whose fixed points correspond to decay points of the
monotone operator. The advantage to an earlier algorithm is demonstrated.
Furthermore an example is given which shows how to analyze a given perturbed
interconnected system.Comment: 30 pages, 7 figures, 4 table
Scaling of stiffness energy for 3d +/-J Ising spin glasses
Large numbers of ground states of 3d EA Ising spin glasses are calculated for
sizes up to 10^3 using a combination of a genetic algorithm and Cluster-Exact
Approximation. A detailed analysis shows that true ground states are obtained.
The ground state stiffness (or domain wall) energy D is calculated. A D ~ L^t
behavior with t=0.19(2) is found which strongly indicates that the 3d model has
an equilibrium spin-glass-paramagnet transition for non-zero T_c.Comment: 4 pages, 4 figure
Visualizing dimensionality reduction of systems biology data
One of the challenges in analyzing high-dimensional expression data is the
detection of important biological signals. A common approach is to apply a
dimension reduction method, such as principal component analysis. Typically,
after application of such a method the data is projected and visualized in the
new coordinate system, using scatter plots or profile plots. These methods
provide good results if the data have certain properties which become visible
in the new coordinate system and which were hard to detect in the original
coordinate system. Often however, the application of only one method does not
suffice to capture all important signals. Therefore several methods addressing
different aspects of the data need to be applied. We have developed a framework
for linear and non-linear dimension reduction methods within our visual
analytics pipeline SpRay. This includes measures that assist the interpretation
of the factorization result. Different visualizations of these measures can be
combined with functional annotations that support the interpretation of the
results. We show an application to high-resolution time series microarray data
in the antibiotic-producing organism Streptomyces coelicolor as well as to
microarray data measuring expression of cells with normal karyotype and cells
with trisomies of human chromosomes 13 and 21
A new method for analyzing ground-state landscapes: ballistic search
A ``ballistic-search'' algorithm is presented which allows the identification
of clusters (or funnels) of ground states in Ising spin glasses even for
moderate system sizes. The clusters are defined to be sets of states, which are
connected in state-space by chains of zero-energy flips of spins. The technique
can also be used to estimate the sizes of such clusters. The performance of the
method is tested with respect to different system sizes and choices of
parameters. As an application the ground-state funnel structure of
two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by
calculating a huge number of ground states per realization. A T=0 entropy per
spin of s_0=0.086(4)k_B is obtained.Comment: 10 pages, 11 figures, 35 references, revte
Calculation of ground states of four-dimensional +or- J Ising spin glasses
Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated
for sizes up to 7x7x7x7 using a combination of a genetic algorithm and
cluster-exact approximation. The ground-state energy of the infinite system is
extrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall)
energy D is calculated. A D~L^{\Theta} behavior with \Theta=0.65(4) is found
which confirms that the d=4 model has an equilibrium spin-glass-paramagnet
transition for non-zero T_c.Comment: 5 pages, 3 figures, 31 references, revtex; update of reference
Ordered phase in the two-dimensional randomly coupled ferromagnet
True ground states are evaluated for a 2d Ising model with random near
neighbor interactions and ferromagnetic second neighbor interactions (the
Randomly Coupled Ferromagnet). The spin glass stiffness exponent is positive
when the absolute value of the random interaction is weaker than the
ferromagnetic interaction. This result demonstrates that in this parameter
domain the spin glass like ordering temperature is non-zero for these systems,
in strong contrast to the 2d Edwards-Anderson spin glass.Comment: 7 pages; 9 figures; revtex; new version much extende
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