1,831 research outputs found
Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem
In this paper, we study linear programming based approaches to the maximum
matching problem in the semi-streaming model. The semi-streaming model has
gained attention as a model for processing massive graphs as the importance of
such graphs has increased. This is a model where edges are streamed-in in an
adversarial order and we are allowed a space proportional to the number of
vertices in a graph.
In recent years, there has been several new results in this semi-streaming
model. However broad techniques such as linear programming have not been
adapted to this model. We present several techniques to adapt and optimize
linear programming based approaches in the semi-streaming model with an
application to the maximum matching problem. As a consequence, we improve
(almost) all previous results on this problem, and also prove new results on
interesting variants
A Time-Space Tradeoff for Triangulations of Points in the Plane
In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm
Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics
The field equations associated with the Born-Infeld-Einstein action are
derived using the Palatini variational technique. In this approach the metric
and connection are varied independently and the Ricci tensor is generally not
symmetric. For sufficiently small curvatures the resulting field equations can
be divided into two sets. One set, involving the antisymmetric part of the
Ricci tensor , consists of the field equation for
a massive vector field. The other set consists of the Einstein field equations
with an energy momentum tensor for the vector field plus additional
corrections. In a vacuum with the field
equations are shown to be the usual Einstein vacuum equations. This extends the
universality of the vacuum Einstein equations, discussed by Ferraris et al.
\cite{Fe1,Fe2}, to the Born-Infeld-Einstein action. In the simplest version of
the theory there is a single coupling constant and by requiring that the
Einstein field equations hold to a good approximation in neutron stars it is
shown that mass of the vector field exceeds the lower bound on the mass of the
photon. Thus, in this case the vector field cannot represent the
electromagnetic field and would describe a new geometrical field. In a more
general version in which the symmetric and antisymmetric parts of the Ricci
tensor have different coupling constants it is possible to satisfy all of the
observational constraints if the antisymmetric coupling is much larger than the
symmetric coupling. In this case the antisymmetric part of the Ricci tensor can
describe the electromagnetic field, although gauge invariance will be broken.Comment: 12 page
Log-periodic self-similarity: an emerging financial law?
A hypothesis that the financial log-periodicity, cascading self-similarity
through various time scales, carries signatures of a law is pursued. It is
shown that the most significant historical financial events can be classified
amazingly well using a single and unique value of the preferred scaling factor
lambda=2, which indicates that its real value should be close to this number.
This applies even to a declining decelerating log-periodic phase. Crucial in
this connection is identification of a "super-bubble" (bubble on bubble)
phenomenon. Identifying a potential "universal" preferred scaling factor, as
undertaken here, may significantly improve the predictive power of the
corresponding methodology. Several more specific related results include
evidence that: (i) the real end of the high technology bubble on the stock
market started (with a decelerating log-periodic draw down) in the begining of
September 2000; (ii) a parallel 2000-2002 decline seen in the Standard & Poor's
500 from the log-periodic perspective is already of the same significance as
the one of the early 1930s and of the late 1970s; (iii) all this points to a
much more serious global crash in around 2025, of course from a level much
higher (at least one order of magnitude) than in 2000.Comment: Talk given by S. Drozdz at International Econophysics Conference,
Bali, August 28-31, 2002; typos correcte
Born-Regulated Gravity in Four Dimensions
Previous work involving Born-regulated gravity theories in two dimensions is
extended to four dimensions. The action we consider has two dimensionful
parameters. Black hole solutions are studied for typical values of these
parameters. For masses above a critical value determined in terms of these
parameters, the event horizon persists. For masses below this critical value,
the event horizon disappears, leaving a ``bare mass'', though of course no
singularity.Comment: LaTeX, 15 pages, 2 figure
A Protocol for Generating Random Elements with their Probabilities
We give an AM protocol that allows the verifier to sample elements x from a
probability distribution P, which is held by the prover. If the prover is
honest, the verifier outputs (x, P(x)) with probability close to P(x). In case
the prover is dishonest, one may hope for the following guarantee: if the
verifier outputs (x, p), then the probability that the verifier outputs x is
close to p. Simple examples show that this cannot be achieved. Instead, we show
that the following weaker condition holds (in a well defined sense) on average:
If (x, p) is output, then p is an upper bound on the probability that x is
output. Our protocol yields a new transformation to turn interactive proofs
where the verifier uses private random coins into proofs with public coins. The
verifier has better running time compared to the well-known Goldwasser-Sipser
transformation (STOC, 1986). For constant-round protocols, we only lose an
arbitrarily small constant in soundness and completeness, while our public-coin
verifier calls the private-coin verifier only once
Maximum Matching in Turnstile Streams
We consider the unweighted bipartite maximum matching problem in the one-pass
turnstile streaming model where the input stream consists of edge insertions
and deletions. In the insertion-only model, a one-pass -approximation
streaming algorithm can be easily obtained with space , where
denotes the number of vertices of the input graph. We show that no such result
is possible if edge deletions are allowed, even if space is
granted, for every . Specifically, for every , we show that in the one-pass turnstile streaming model, in order to compute
a -approximation, space is
required for constant error randomized algorithms, and, up to logarithmic
factors, space is sufficient. Our lower bound result is
proved in the simultaneous message model of communication and may be of
independent interest
Stochastics theory of log-periodic patterns
We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge
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