1,197 research outputs found

### RiffleScrambler - a memory-hard password storing function

We introduce RiffleScrambler: a new family of directed acyclic graphs and a
corresponding data-independent memory hard function with password independent
memory access. We prove its memory hardness in the random oracle model.
RiffleScrambler is similar to Catena -- updates of hashes are determined by a
graph (bit-reversal or double-butterfly graph in Catena). The advantage of the
RiffleScrambler over Catena is that the underlying graphs are not predefined
but are generated per salt, as in Balloon Hashing. Such an approach leads to
higher immunity against practical parallel attacks. RiffleScrambler offers
better efficiency than Balloon Hashing since the in-degree of the underlying
graph is equal to 3 (and is much smaller than in Ballon Hashing). At the same
time, because the underlying graph is an instance of a Superconcentrator, our
construction achieves the same time-memory trade-offs.Comment: Accepted to ESORICS 201

### Percolation-like Scaling Exponents for Minimal Paths and Trees in the Stochastic Mean Field Model

In the mean field (or random link) model there are $n$ points and inter-point
distances are independent random variables. For $0 < \ell < \infty$ and in the
$n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number of steps
in a path whose average step-length is $\leq \ell$). The function
$\delta(\ell)$ is analogous to the percolation function in percolation theory:
there is a critical value $\ell_* = e^{-1}$ at which $\delta(\cdot)$ becomes
non-zero, and (presumably) a scaling exponent $\beta$ in the sense
$\delta(\ell) \asymp (\ell - \ell_*)^\beta$. Recently developed probabilistic
methodology (in some sense a rephrasing of the cavity method of Mezard-Parisi)
provides a simple albeit non-rigorous way of writing down such functions in
terms of solutions of fixed-point equations for probability distributions.
Solving numerically gives convincing evidence that $\beta = 3$. A parallel
study with trees instead of paths gives scaling exponent $\beta = 2$. The new
exponents coincide with those found in a different context (comparing optimal
and near-optimal solutions of mean-field TSP and MST) and reinforce the
suggestion that these scaling exponents determine universality classes for
optimization problems on random points.Comment: 19 page

### Epitaxial growth and surface reconstruction of CrSb(0001)

Smooth CrSb(0001) films have been grown by molecular beam epitaxy on MnSb(0001) – GaAs(111) substrates. CrSb(0001) shows (2 × 2), triple domain (1 × 4) and (√3×√3)R30° reconstructed surfaces as well as a (1 × 1) phase. The dependence of reconstruction on substrate temperature and incident fluxes is very similar to MnSb(0001)

### Scaling and Universality in Continuous Length Combinatorial Optimization

We consider combinatorial optimization problems defined over random
ensembles, and study how solution cost increases when the optimal solution
undergoes a small perturbation delta. For the minimum spanning tree, the
increase in cost scales as delta^2; for the mean-field and Euclidean minimum
matching and traveling salesman problems in dimension d>=2, the increase scales
as delta^3; this is observed in Monte Carlo simulations in d=2,3,4 and in
theoretical analysis of a mean-field model. We speculate that the scaling
exponent could serve to classify combinatorial optimization problems into a
small number of distinct categories, similar to universality classes in
statistical physics.Comment: 5 pages; 3 figure

### Routed Planar Networks

Modeling a road network as a planar graph seems very natural. However, in studying continuum limits of such networks it is useful to take {\em routes} rather than {\em edges} as primitives. This article is intended to introduce the relevant (discrete setting) notion of {\em routed network} to graph theorists. We give a naive classification of all 71 topologically different such networks on 4 leaves, and pose a variety of challenging research questions

### Ground States for Exponential Random Graphs

We propose a perturbative method to estimate the normalization constant in
exponential random graph models as the weighting parameters approach infinity.
As an application, we give evidence of discontinuity in natural parametrization
along the critical directions of the edge-triangle model.Comment: 12 pages, 3 figures, 1 tabl

### Multicritical continuous random trees

We introduce generalizations of Aldous' Brownian Continuous Random Tree as
scaling limits for multicritical models of discrete trees. These discrete
models involve trees with fine-tuned vertex-dependent weights ensuring a k-th
root singularity in their generating function. The scaling limit involves
continuous trees with branching points of order up to k+1. We derive explicit
integral representations for the average profile of this k-th order
multicritical continuous random tree, as well as for its history distributions
measuring multi-point correlations. The latter distributions involve
non-positive universal weights at the branching points together with fractional
derivative couplings. We prove universality by rederiving the same results
within a purely continuous axiomatic approach based on the resolution of a set
of consistency relations for the multi-point correlations. The average profile
is shown to obey a fractional differential equation whose solution involves
hypergeometric functions and matches the integral formula of the discrete
approach.Comment: 34 pages, 12 figures, uses lanlmac, hyperbasics, eps

### Optimal spatial transportation networks where link-costs are sublinear in link-capacity

Consider designing a transportation network on $n$ vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length $\ell$ and capacity $c$ scales as $\ell c^\beta$ for fixed
$0<\beta<1$. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as $n^{\alpha(\beta)}$, where $\alpha(\beta)
= 1 - \frac{\beta}{2}$ on $0 < \beta \leq {1/2}$ and $\alpha(\beta) = {1/2} +
\frac{\beta}{2}$ on ${1/2} \leq \beta < 1$. This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only $1 + o(1)$ times
average straight line length. The transition at $\beta = {1/2}$ corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed $s$ and the
cost becomes $\ell c^\beta s^\gamma$.Comment: 13 page

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