22,145 research outputs found
Synchronous Counting and Computational Algorithm Design
Consider a complete communication network on nodes, each of which is a
state machine. In synchronous 2-counting, the nodes receive a common clock
pulse and they have to agree on which pulses are "odd" and which are "even". We
require that the solution is self-stabilising (reaching the correct operation
from any initial state) and it tolerates Byzantine failures (nodes that
send arbitrary misinformation). Prior algorithms are expensive to implement in
hardware: they require a source of random bits or a large number of states.
This work consists of two parts. In the first part, we use computational
techniques (often known as synthesis) to construct very compact deterministic
algorithms for the first non-trivial case of . While no algorithm exists
for , we show that as few as 3 states per node are sufficient for all
values . Moreover, the problem cannot be solved with only 2 states per
node for , but there is a 2-state solution for all values .
In the second part, we develop and compare two different approaches for
synthesising synchronous counting algorithms. Both approaches are based on
casting the synthesis problem as a propositional satisfiability (SAT) problem
and employing modern SAT-solvers. The difference lies in how to solve the SAT
problem: either in a direct fashion, or incrementally within a counter-example
guided abstraction refinement loop. Empirical results suggest that the former
technique is more efficient if we want to synthesise time-optimal algorithms,
while the latter technique discovers non-optimal algorithms more quickly.Comment: 35 pages, extended and revised versio
System Description for a Scalable, Fault-Tolerant, Distributed Garbage Collector
We describe an efficient and fault-tolerant algorithm for distributed cyclic
garbage collection. The algorithm imposes few requirements on the local
machines and allows for flexibility in the choice of local collector and
distributed acyclic garbage collector to use with it. We have emphasized
reducing the number and size of network messages without sacrificing the
promptness of collection throughout the algorithm. Our proposed collector is a
variant of back tracing to avoid extensive synchronization between machines. We
have added an explicit forward tracing stage to the standard back tracing stage
and designed a tuned heuristic to reduce the total amount of work done by the
collector. Of particular note is the development of fault-tolerant cooperation
between traces and a heuristic that aggressively reduces the set of suspect
objects.Comment: 47 pages, LaTe
Incremental garbage collection in massive object stores
© 2001 IEEEThere are only a few garbage collection algorithms that have been designed to operate over massive object stores. These algorithms operate at two levels, locally via incremental collection of small partitions and globally via detection of cross partition garbage, including cyclic garbage. At each level there is a choice of collection mechanism. For example, the PMOS collector employs tracing at the local level and reference counting at the global level. Another approach implemented in the Thor object database uses tracing at both levels. In this paper we present two new algorithms that both employ reference counting at the local level. One algorithm uses reference counting at the higher level and the other uses tracing at the higher level. An evaluation strategy is presented to support comparisons between these four algorithms and preliminary experiments are outlined
Eigenvalue-based Cyclostationary Spectrum Sensing Using Multiple Antennas
In this paper, we propose a signal-selective spectrum sensing method for
cognitive radio networks and specifically targeted for receivers with
multiple-antenna capability. This method is used for detecting the presence or
absence of primary users based on the eigenvalues of the cyclic covariance
matrix of received signals. In particular, the cyclic correlation significance
test is used to detect a specific signal-of-interest by exploiting knowledge of
its cyclic frequencies. The analytical threshold for achieving constant false
alarm rate using this detection method is presented, verified through
simulations, and shown to be independent of both the number of samples used and
the noise variance, effectively eliminating the dependence on accurate noise
estimation. The proposed method is also shown, through numerical simulations,
to outperform existing multiple-antenna cyclostationary-based spectrum sensing
algorithms under a quasi-static Rayleigh fading channel, in both spatially
correlated and uncorrelated noise environments. The algorithm also has
significantly lower computational complexity than these other approaches.Comment: 6 pages, 6 figures, accepted to IEEE GLOBECOM 201
Pruning Algorithms for Pretropisms of Newton Polytopes
Pretropisms are candidates for the leading exponents of Puiseux series that
represent solutions of polynomial systems. To find pretropisms, we propose an
exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton
polytopes. We prefer exact arithmetic not only because of the exact input and
the degrees of the output, but because of the often unpredictable growth of the
coordinates in the face normals, even for polytopes in generic position. We
provide experimental results with our preliminary implementation in Sage that
compare favorably with the pruning method that relies only on cone
intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning,
accepted for presentation at Computer Algebra in Scientific Computing, CASC
201
Estimation under group actions: recovering orbits from invariants
Motivated by geometric problems in signal processing, computer vision, and
structural biology, we study a class of orbit recovery problems where we
observe very noisy copies of an unknown signal, each acted upon by a random
element of some group (such as Z/p or SO(3)). The goal is to recover the orbit
of the signal under the group action in the high-noise regime. This generalizes
problems of interest such as multi-reference alignment (MRA) and the
reconstruction problem in cryo-electron microscopy (cryo-EM). We obtain
matching lower and upper bounds on the sample complexity of these problems in
high generality, showing that the statistical difficulty is intricately
determined by the invariant theory of the underlying symmetry group.
In particular, we determine that for cryo-EM with noise variance
and uniform viewing directions, the number of samples required scales as
. We match this bound with a novel algorithm for ab initio
reconstruction in cryo-EM, based on invariant features of degree at most 3. We
further discuss how to recover multiple molecular structures from heterogeneous
cryo-EM samples.Comment: 54 pages. This version contains a number of new result
- …