341 research outputs found
A Repair Framework for Scalar MDS Codes
Several works have developed vector-linear maximum-distance separable (MDS)
storage codes that min- imize the total communication cost required to repair a
single coded symbol after an erasure, referred to as repair bandwidth (BW).
Vector codes allow communicating fewer sub-symbols per node, instead of the
entire content. This allows non trivial savings in repair BW. In sharp
contrast, classic codes, like Reed- Solomon (RS), used in current storage
systems, are deemed to suffer from naive repair, i.e. downloading the entire
stored message to repair one failed node. This mainly happens because they are
scalar-linear. In this work, we present a simple framework that treats scalar
codes as vector-linear. In some cases, this allows significant savings in
repair BW. We show that vectorized scalar codes exhibit properties that
simplify the design of repair schemes. Our framework can be seen as a finite
field analogue of real interference alignment. Using our simplified framework,
we design a scheme that we call clique-repair which provably identifies the
best linear repair strategy for any scalar 2-parity MDS code, under some
conditions on the sub-field chosen for vectorization. We specify optimal repair
schemes for specific (5,3)- and (6,4)-Reed- Solomon (RS) codes. Further, we
present a repair strategy for the RS code currently deployed in the Facebook
Analytics Hadoop cluster that leads to 20% of repair BW savings over naive
repair which is the repair scheme currently used for this code.Comment: 10 Pages; accepted to IEEE JSAC -Distributed Storage 201
An updated survey on rainbow connections of graphs - a dynamic survey
The concept of rainbow connection was introduced by Chartrand, Johns, McKeon and Zhang in 2008. Nowadays it has become a new and active subject in graph theory. There is a book on this topic by Li and Sun in 2012, and a survey paper by Li, Shi and Sun in 2013. More and more researchers are working in this field, and many new papers have been published in journals. In this survey we attempt to bring together most of the new results and papers that deal with this topic. We begin with an introduction, and then try to organize the work into the following categories, rainbow connection coloring of edge-version, rainbow connection coloring of vertex-version, rainbow -connectivity, rainbow index, rainbow connection coloring of total-version, rainbow connection on digraphs, rainbow connection on hypergraphs. This survey also contains some conjectures, open problems and questions for further study
08431 Abstracts Collection -- Moderately Exponential Time Algorithms
From to , the Dagstuhl Seminar 08431 ``Moderately Exponential Time Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Fundamental Limits of Nanophotonic Design
Nanoscale fabrication techniques, computational inverse design, and fields
from silicon photonics to metasurface optics are enabling transformative use of
an unprecedented number of structural degrees of freedom in nanophotonics. A
critical need is to understand the extreme limits to what is possible by
engineering nanophotonic structures. This thesis establishes the first general
theoretical framework identifying fundamental limits to light--matter
interactions. It derives bounds for applications across nanophotonics,
including far-field scattering, optimal wavefront shaping, optical beam
switching, and wave communication, as well as the miniaturization of optical
components, including perfect absorbers, linear optical analog computing units,
resonant optical sensors, multilayered thin films, and high-NA metalenses. The
bounds emerge from an infinite set of physical constraints that have to be
satisfied by polarization fields in response to an excitation. The constraints
encode power conservation in single-scenario scattering and requisite field
correlations in multi-scenario scattering. The framework developed in this
thesis, encompassing general linear wave scattering dynamics, offers a new way
to understand optimal designs and their fundamental limits, in nanophotonics
and beyond.Comment: PhD thesi
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Extracting Data-Level Parallelism in High-Level Synthesis for Reconfigurable Architectures
High-Level Synthesis (HLS) tools are a set of algorithms that allow programmers to obtain implementable Hardware Description Language (HDL) code from specifications written high-level, sequential languages such as C, C++, or Java. HLS has allowed programmers to code in their preferred language while still obtaining all the benefits hardware acceleration has to offer without them needing to be intimately familiar with the hardware platform of the accelerator. In this work we summarize and expand upon several of our approaches to improve the automatic memory banking capabilities of HLS tools targeting reconfigurable architectures, namely Field-Programmable Gate Arrays or FPGA\u27s. We explored several approaches to automatically find the optimal partition factor and a usable banking scheme for stencil kernels including a tessellation based approach using multiple families of hyperplanes to do the partitioning which was able to find a better banking factor than current state-of-the-art methods and a graph theory methodology that allowed us to mathematically prove the optimality of our banking solutions. For non-stencil kernels we relaxed some of the conditions in our graph-based model to propose a best-effort solution to arbitrarily reduce memory access conflicts (simultaneous accesses to the same memory bank). We also proposed a non-linear transformation using prime factorization to convert a small subset of non-stencil kernels into stencil memory accesses, allowing us to use all previous work in memory partition to them. Our approaches were able to obtain better results than commercial tools and state-of-the-art algorithms in terms of reduced resource utilization and increased frequency of operation. We were also able to obtain better partition factors for some stencil kernels and usable baking schemes for non-stencil kernels with better performance than any applicable existing algorithm
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