3,421 research outputs found
Solving MaxSAT and #SAT on structured CNF formulas
In this paper we propose a structural parameter of CNF formulas and use it to
identify instances of weighted MaxSAT and #SAT that can be solved in polynomial
time. Given a CNF formula we say that a set of clauses is precisely satisfiable
if there is some complete assignment satisfying these clauses only. Let the
ps-value of the formula be the number of precisely satisfiable sets of clauses.
Applying the notion of branch decompositions to CNF formulas and using ps-value
as cut function, we define the ps-width of a formula. For a formula given with
a decomposition of polynomial ps-width we show dynamic programming algorithms
solving weighted MaxSAT and #SAT in polynomial time. Combining with results of
'Belmonte and Vatshelle, Graph classes with structured neighborhoods and
algorithmic applications, Theor. Comput. Sci. 511: 54-65 (2013)' we get
polynomial-time algorithms solving weighted MaxSAT and #SAT for some classes of
structured CNF formulas. For example, we get algorithms for
formulas of clauses and variables and size , if has a linear
ordering of the variables and clauses such that for any variable occurring
in clause , if appears before then any variable between them also
occurs in , and if appears before then occurs also in any clause
between them. Note that the class of incidence graphs of such formulas do not
have bounded clique-width
Efficient Decomposed Learning for Structured Prediction
Structured prediction is the cornerstone of several machine learning
applications. Unfortunately, in structured prediction settings with expressive
inter-variable interactions, exact inference-based learning algorithms, e.g.
Structural SVM, are often intractable. We present a new way, Decomposed
Learning (DecL), which performs efficient learning by restricting the inference
step to a limited part of the structured spaces. We provide characterizations
based on the structure, target parameters, and gold labels, under which DecL is
equivalent to exact learning. We then show that in real world settings, where
our theoretical assumptions may not completely hold, DecL-based algorithms are
significantly more efficient and as accurate as exact learning.Comment: ICML201
Approximating Minimum Independent Dominating Sets in Wireless Networks
We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a (1+")- pproximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network
Learning parametric dictionaries for graph signals
In sparse signal representation, the choice of a dictionary often involves a
tradeoff between two desirable properties -- the ability to adapt to specific
signal data and a fast implementation of the dictionary. To sparsely represent
signals residing on weighted graphs, an additional design challenge is to
incorporate the intrinsic geometric structure of the irregular data domain into
the atoms of the dictionary. In this work, we propose a parametric dictionary
learning algorithm to design data-adapted, structured dictionaries that
sparsely represent graph signals. In particular, we model graph signals as
combinations of overlapping local patterns. We impose the constraint that each
dictionary is a concatenation of subdictionaries, with each subdictionary being
a polynomial of the graph Laplacian matrix, representing a single pattern
translated to different areas of the graph. The learning algorithm adapts the
patterns to a training set of graph signals. Experimental results on both
synthetic and real datasets demonstrate that the dictionaries learned by the
proposed algorithm are competitive with and often better than unstructured
dictionaries learned by state-of-the-art numerical learning algorithms in terms
of sparse approximation of graph signals. In contrast to the unstructured
dictionaries, however, the dictionaries learned by the proposed algorithm
feature localized atoms and can be implemented in a computationally efficient
manner in signal processing tasks such as compression, denoising, and
classification
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