26,456 research outputs found
On Sparsification for Computing Treewidth
We investigate whether an n-vertex instance (G,k) of Treewidth, asking
whether the graph G has treewidth at most k, can efficiently be made sparse
without changing its answer. By giving a special form of OR-cross-composition,
we prove that this is unlikely: if there is an e > 0 and a polynomial-time
algorithm that reduces n-vertex Treewidth instances to equivalent instances, of
an arbitrary problem, with O(n^{2-e}) bits, then NP is in coNP/poly and the
polynomial hierarchy collapses to its third level.
Our sparsification lower bound has implications for structural
parameterizations of Treewidth: parameterizations by measures that do not
exceed the vertex count, cannot have kernels with O(k^{2-e}) bits for any e >
0, unless NP is in coNP/poly. Motivated by the question of determining the
optimal kernel size for Treewidth parameterized by vertex cover, we improve the
O(k^3)-vertex kernel from Bodlaender et al. (STACS 2011) to a kernel with
O(k^2) vertices. Our improved kernel is based on a novel form of
treewidth-invariant set. We use the q-expansion lemma of Fomin et al. (STACS
2011) to find such sets efficiently in graphs whose vertex count is
superquadratic in their vertex cover number.Comment: 21 pages. Full version of the extended abstract presented at IPEC
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Kerr-Schild metrics revisited I. The ground state
The Kerr-Schild pencil of metrics g_{ab}+\La l_al_b is investigated in the
generic case when it maps an arbitrary vacuum space-time with metric
to a vacuum space-time. The theorem is proved that this generic case, with the
field shearing, does not contain the shear-free subclass as a smooth limit.
It is shown that one of the K\'ota-Perj\'es metrics is a solution in the
shearing class.Comment: 16 page
Perfect state distinguishability and computational speedups with postselected closed timelike curves
Bennett and Schumacher's postselected quantum teleportation is a model of
closed timelike curves (CTCs) that leads to results physically different from
Deutsch's model. We show that even a single qubit passing through a
postselected CTC (P-CTC) is sufficient to do any postselected quantum
measurement, and we discuss an important difference between "Deutschian" CTCs
(D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the
present outcome of an experiment. Then, based on a suggestion of Bennett and
Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set
of linearly independent quantum states, and we prove that it is not possible
for such a party to distinguish a set of linearly dependent states. The power
of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still
applies to circuits using them regardless of their ability to conspire in
violating the uncertainty principle. We then discuss how different notions of a
quantum mixture that are indistinguishable in linear quantum mechanics lead to
dramatically differing conclusions in a nonlinear quantum mechanics involving
P-CTCs. Finally, we give explicit circuit constructions that can efficiently
factor integers, efficiently solve any decision problem in the intersection of
NP and coNP, and probabilistically solve any decision problem in NP. These
circuits accomplish these tasks with just one qubit traveling back in time, and
they exploit the ability of postselected closed timelike curves to create
grandfather paradoxes for invalid answers.Comment: 15 pages, 4 figures; Foundations of Physics (2011
Stigmergic hyperlink's contributes to web search
Stigmergic hyperlinks are hyperlinks with a "heart beat": if used they stay healthy and online; if
neglected, they fade, eventually getting replaced. Their life attribute is a relative usage measure that
regular hyperlinks do not provide, hence PageRank-like measures have historically been well
informed about the structure of webs of documents, but unaware of what users effectively do with
the links.
This paper elaborates on how to input the users’ perspective into Google’s original, structure centric,
PageRank metric. The discussion then bridges to the Deep Web, some search challenges, and how
stigmergic hyperlinks could help decentralize the search experience, facilitating user generated
search solutions and supporting new related business models.info:eu-repo/semantics/publishedVersio
Principles and Implementation of Deductive Parsing
We present a system for generating parsers based directly on the metaphor of
parsing as deduction. Parsing algorithms can be represented directly as
deduction systems, and a single deduction engine can interpret such deduction
systems so as to implement the corresponding parser. The method generalizes
easily to parsers for augmented phrase structure formalisms, such as
definite-clause grammars and other logic grammar formalisms, and has been used
for rapid prototyping of parsing algorithms for a variety of formalisms
including variants of tree-adjoining grammars, categorial grammars, and
lexicalized context-free grammars.Comment: 69 pages, includes full Prolog cod
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