1,072 research outputs found
Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford
A \emph{metric tree embedding} of expected \emph{stretch~}
maps a weighted -node graph to a weighted tree with such that, for all ,
and
. Such embeddings are highly useful for designing
fast approximation algorithms, as many hard problems are easy to solve on tree
instances. However, to date the best parallel -depth algorithm that achieves an asymptotically optimal expected stretch of
requires
work and a metric as input.
In this paper, we show how to achieve the same guarantees using
depth and
work, where and is an arbitrarily small constant.
Moreover, one may further reduce the work to at the expense of increasing the expected stretch to
.
Our main tool in deriving these parallel algorithms is an algebraic
characterization of a generalization of the classic Moore-Bellman-Ford
algorithm. We consider this framework, which subsumes a variety of previous
"Moore-Bellman-Ford-like" algorithms, to be of independent interest and discuss
it in depth. In our tree embedding algorithm, we leverage it for providing
efficient query access to an approximate metric that allows sampling the tree
using depth and work.
We illustrate the generality and versatility of our techniques by various
examples and a number of additional results
Hybrid expansions for local structural relaxations
A model is constructed in which pair potentials are combined with the cluster
expansion method in order to better describe the energetics of structurally
relaxed substitutional alloys. The effect of structural relaxations away from
the ideal crystal positions, and the effect of ordering is described by
interatomic-distance dependent pair potentials, while more subtle
configurational aspects associated with correlations of three- and more sites
are described purely within the cluster expansion formalism. Implementation of
such a hybrid expansion in the context of the cluster variation method or Monte
Carlo method gives improved ability to model phase stability in alloys from
first-principles.Comment: 8 pages, 1 figur
Recommended from our members
Containment and equivalence of weighted automata: Probabilistic and max-plus cases
This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain
Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the
state-complexity of representing sub- or superword closures of context-free
grammars (CFGs): (1) We prove a (tight) upper bound of on
the size of nondeterministic finite automata (NFAs) representing the subword
closure of a CFG of size . (2) We present a family of CFGs for which the
minimal deterministic finite automata representing their subword closure
matches the upper-bound of following from (1).
Furthermore, we prove that the inequivalence problem for NFAs representing sub-
or superword-closed languages is only NP-complete as opposed to PSPACE-complete
for general NFAs. Finally, we extend our results into an approximation method
to attack inequivalence problems for CFGs
An efficient synthesis of procyanidins. Rare earth metal Lewis acid catalyzed equimolar condensation of catechin and epicatechin
ArticleTETRAHEDRON LETTERS. 48(33): 5891-5894 (2007)journal articl
Signal, noise power spectrum, and detective quantum efficiency of indirectĂą detection flatĂą panel imagers for diagnostic radiology
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135120/1/mp8243.pd
Fatigue strengthening of damaged steel members using wire arc additive manufacturing
In this study, a directed energy deposition (DED) process called wire arc additive manufacturing (WAAM) is employed for the fatigue strengthening of damaged steel members. Three steel specimens with central cracks were tested under a high-cycle fatigue loading (HCF) regime: (1) the reference specimen; (2) the WAAM-repaired specimen with an as-deposited profile, and (3) the WAAM-repaired specimen machined to reduce stress concentration factors (SCF). The corresponding finite element (FE) simulation of the WAAM process was calibrated using static experimental results, which revealed the main mechanism. The process was found to introduce compressive residual stresses at the crack tip owing to the thermal contraction of the repair. The FE results also revealed that stress concentration exists at the root of the as-deposited WAAM; this stress concentration can be mitigated by machining the WAAM to a pyramid-like shape. The fractography analysis indicated that the cracks were initiated at the WAAM-steel interface, and microscopic observations revealed that the microcracks were arrested by the porosities in the melted interface. The results of this pioneering study suggest that WAAM repair is a promising technique for combating fatigue damage in steel structures
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