3,786 research outputs found
Quantum symmetries and exceptional collections
We study the interplay between discrete quantum symmetries at certain points
in the moduli space of Calabi-Yau compactifications, and the associated
identities that the geometric realization of D-brane monodromies must satisfy.
We show that in a wide class of examples, both local and compact, the monodromy
identities in question always follow from a single mathematical statement. One
of the simplest examples is the Z_5 symmetry at the Gepner point of the
quintic, and the associated D-brane monodromy identity
Deterministic and Probabilistic Binary Search in Graphs
We consider the following natural generalization of Binary Search: in a given
undirected, positively weighted graph, one vertex is a target. The algorithm's
task is to identify the target by adaptively querying vertices. In response to
querying a node , the algorithm learns either that is the target, or is
given an edge out of that lies on a shortest path from to the target.
We study this problem in a general noisy model in which each query
independently receives a correct answer with probability (a
known constant), and an (adversarial) incorrect one with probability .
Our main positive result is that when (i.e., all answers are
correct), queries are always sufficient. For general , we give an
(almost information-theoretically optimal) algorithm that uses, in expectation,
no more than queries, and identifies the target correctly with probability at
leas . Here, denotes the
entropy. The first bound is achieved by the algorithm that iteratively queries
a 1-median of the nodes not ruled out yet; the second bound by careful repeated
invocations of a multiplicative weights algorithm.
Even for , we show several hardness results for the problem of
determining whether a target can be found using queries. Our upper bound of
implies a quasipolynomial-time algorithm for undirected connected
graphs; we show that this is best-possible under the Strong Exponential Time
Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs
with non-uniform node querying costs, the problem is PSPACE-complete. For a
semi-adaptive version, in which one may query nodes each in rounds, we
show membership in in the polynomial hierarchy, and hardness
for
Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable
There has been significant recent interest in parallel graph processing due
to the need to quickly analyze the large graphs available today. Many graph
codes have been designed for distributed memory or external memory. However,
today even the largest publicly-available real-world graph (the Hyperlink Web
graph with over 3.5 billion vertices and 128 billion edges) can fit in the
memory of a single commodity multicore server. Nevertheless, most experimental
work in the literature report results on much smaller graphs, and the ones for
the Hyperlink graph use distributed or external memory. Therefore, it is
natural to ask whether we can efficiently solve a broad class of graph problems
on this graph in memory.
This paper shows that theoretically-efficient parallel graph algorithms can
scale to the largest publicly-available graphs using a single machine with a
terabyte of RAM, processing them in minutes. We give implementations of
theoretically-efficient parallel algorithms for 20 important graph problems. We
also present the optimizations and techniques that we used in our
implementations, which were crucial in enabling us to process these large
graphs quickly. We show that the running times of our implementations
outperform existing state-of-the-art implementations on the largest real-world
graphs. For many of the problems that we consider, this is the first time they
have been solved on graphs at this scale. We have made the implementations
developed in this work publicly-available as the Graph-Based Benchmark Suite
(GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium
on Parallelism in Algorithms and Architectures (SPAA), 201
MIMO free-space optical communication employing subcarrier intensity modulation in atmospheric turbulence channels
In this paper, we analyse the error performance of transmitter/receiver array free-space optical (FSO) communication system employing binary phase shift keying (BPSK) subcarrier intensity modulation (SIM) in clear but turbulent atmospheric channel. Subcarrier modulation is employed to eliminate the need for adaptive threshold detector. Direct detection is employed at the receiver and each subcarrier is subsequently demodulated coherently. The effect of irradiance fading is mitigated with an array of lasers and photodetectors. The received signals are linearly combined using the optimal maximum ratio combining (MRC), the equal gain combining (EGC) and the selection combining (SelC). The bit error rate (BER) equations are derived considering additive white Gaussian noise and log normal intensity fluctuations. This work is part of the EU COST actions and EU projects
Optimal Vertex Cover for the Small-World Hanoi Networks
The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with
an exact renormalization group and parallel-tempering Monte Carlo simulations.
The grand canonical partition function of the equivalent hard-core repulsive
lattice-gas problem is recast first as an Ising-like canonical partition
function, which allows for a closed set of renormalization group equations. The
flow of these equations is analyzed for the limit of infinite chemical
potential, at which the vertex-cover problem is attained. The relevant fixed
point and its neighborhood are analyzed, and non-trivial results are obtained
both, for the coverage as well as for the ground state entropy density, which
indicates the complex structure of the solution space. Using special
hierarchy-dependent operators in the renormalization group and Monte-Carlo
simulations, structural details of optimal configurations are revealed. These
studies indicate that the optimal coverages (or packings) are not related by a
simple symmetry. Using a clustering analysis of the solutions obtained in the
Monte Carlo simulations, a complex solution space structure is revealed for
each system size. Nevertheless, in the thermodynamic limit, the solution
landscape is dominated by one huge set of very similar solutions.Comment: RevTex, 24 pages; many corrections in text and figures; final
version; for related information, see
http://www.physics.emory.edu/faculty/boettcher
A Two-loop Test of Buscher's T-duality I
We study the two loop quantum equivalence of sigma models related by
Buscher's T-duality transformation. The computation of the two loop
perturbative free energy density is performed in the case of a certain
deformation of the SU(2) principal sigma model, and its T-dual, using
dimensional regularization and the geometric sigma model perturbation theory.
We obtain agreement between the free energy density expressions of the two
models.Comment: 28 pp, Latex, references adde
Routing Games over Time with FIFO policy
We study atomic routing games where every agent travels both along its
decided edges and through time. The agents arriving on an edge are first lined
up in a \emph{first-in-first-out} queue and may wait: an edge is associated
with a capacity, which defines how many agents-per-time-step can pop from the
queue's head and enter the edge, to transit for a fixed delay. We show that the
best-response optimization problem is not approximable, and that deciding the
existence of a Nash equilibrium is complete for the second level of the
polynomial hierarchy. Then, we drop the rationality assumption, introduce a
behavioral concept based on GPS navigation, and study its worst-case efficiency
ratio to coordination.Comment: Submission to WINE-2017 Deadline was August 2nd AoE, 201
The Complexity of Routing with Few Collisions
We study the computational complexity of routing multiple objects through a
network in such a way that only few collisions occur: Given a graph with
two distinct terminal vertices and two positive integers and , the
question is whether one can connect the terminals by at least routes (e.g.
paths) such that at most edges are time-wise shared among them. We study
three types of routes: traverse each vertex at most once (paths), each edge at
most once (trails), or no such restrictions (walks). We prove that for paths
and trails the problem is NP-complete on undirected and directed graphs even if
is constant or the maximum vertex degree in the input graph is constant.
For walks, however, it is solvable in polynomial time on undirected graphs for
arbitrary and on directed graphs if is constant. We additionally study
for all route types a variant of the problem where the maximum length of a
route is restricted by some given upper bound. We prove that this
length-restricted variant has the same complexity classification with respect
to paths and trails, but for walks it becomes NP-complete on undirected graphs
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