68,258 research outputs found
Comprehending Kademlia Routing - A Theoretical Framework for the Hop Count Distribution
The family of Kademlia-type systems represents the most efficient and most
widely deployed class of internet-scale distributed systems. Its success has
caused plenty of large scale measurements and simulation studies, and several
improvements have been introduced. Its character of parallel and
non-deterministic lookups, however, so far has prevented any concise formal
analysis. This paper introduces the first comprehensive formal model of the
routing of the entire family of systems that is validated against previous
measurements. It sheds light on the overall hop distribution and lookup delays
of the different variations of the original protocol. It additionally shows
that several of the recent improvements to the protocol in fact have been
counter-productive and identifies preferable designs with regard to routing
overhead and resilience.Comment: 12 pages, 6 figure
Parallel Algorithms for Summing Floating-Point Numbers
The problem of exactly summing n floating-point numbers is a fundamental
problem that has many applications in large-scale simulations and computational
geometry. Unfortunately, due to the round-off error in standard floating-point
operations, this problem becomes very challenging. Moreover, all existing
solutions rely on sequential algorithms which cannot scale to the huge datasets
that need to be processed.
In this paper, we provide several efficient parallel algorithms for summing n
floating point numbers, so as to produce a faithfully rounded floating-point
representation of the sum. We present algorithms in PRAM, external-memory, and
MapReduce models, and we also provide an experimental analysis of our MapReduce
algorithms, due to their simplicity and practical efficiency.Comment: Conference version appears in SPAA 201
OneMax in Black-Box Models with Several Restrictions
Black-box complexity studies lower bounds for the efficiency of
general-purpose black-box optimization algorithms such as evolutionary
algorithms and other search heuristics. Different models exist, each one being
designed to analyze a different aspect of typical heuristics such as the memory
size or the variation operators in use. While most of the previous works focus
on one particular such aspect, we consider in this work how the combination of
several algorithmic restrictions influence the black-box complexity. Our
testbed are so-called OneMax functions, a classical set of test functions that
is intimately related to classic coin-weighing problems and to the board game
Mastermind.
We analyze in particular the combined memory-restricted ranking-based
black-box complexity of OneMax for different memory sizes. While its isolated
memory-restricted as well as its ranking-based black-box complexity for bit
strings of length is only of order , the combined model does not
allow for algorithms being faster than linear in , as can be seen by
standard information-theoretic considerations. We show that this linear bound
is indeed asymptotically tight. Similar results are obtained for other memory-
and offspring-sizes. Our results also apply to the (Monte Carlo) complexity of
OneMax in the recently introduced elitist model, in which only the best-so-far
solution can be kept in the memory. Finally, we also provide improved lower
bounds for the complexity of OneMax in the regarded models.
Our result enlivens the quest for natural evolutionary algorithms optimizing
OneMax in iterations.Comment: This is the full version of a paper accepted to GECCO 201
Small Depth Quantum Circuits
Small depth quantum circuits have proved to be unexpectedly powerful in comparison to their classical counterparts. We survey some of the recent work on this and present some open problems.National Security Agency; Advanced Research and Development Agency under Army Research Office (DAAD 19-02-1-0058
A Lower Bound Technique for Communication in BSP
Communication is a major factor determining the performance of algorithms on
current computing systems; it is therefore valuable to provide tight lower
bounds on the communication complexity of computations. This paper presents a
lower bound technique for the communication complexity in the bulk-synchronous
parallel (BSP) model of a given class of DAG computations. The derived bound is
expressed in terms of the switching potential of a DAG, that is, the number of
permutations that the DAG can realize when viewed as a switching network. The
proposed technique yields tight lower bounds for the fast Fourier transform
(FFT), and for any sorting and permutation network. A stronger bound is also
derived for the periodic balanced sorting network, by applying this technique
to suitable subnetworks. Finally, we demonstrate that the switching potential
captures communication requirements even in computational models different from
BSP, such as the I/O model and the LPRAM
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