72 research outputs found
Set-based approach to passenger aircraft family design
Presented is a method for the design of passenger aircraft families. Existing point-based methods found in the literature employ sequential approaches in which a single design solution is selected early and is then iteratively modified until all requirements are satisfied. The challenge with such approaches is that the design is driven toward a solution that, although promising to the optimizer, may be infeasible due to factors not considered by the models. The proposed method generates multiple solutions at the outset. Then, the infeasible solutions are discarded gradually through constraint satisfaction and set intersection. The method has been evaluated through a notional example of a three-member aircraft family design. The conclusion is that point-based design is still seen as preferable for incremental (conventional) designs based on a wealth of validated empirical methods, whereas the proposed approach, although resource-intensive, is seen as more suited to innovative designs
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
We introduce the notion of the stopping redundancy hierarchy of a linear
block code as a measure of the trade-off between performance and complexity of
iterative decoding for the binary erasure channel. We derive lower and upper
bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and
Bonferroni-type inequalities, and specialize them for codes with cyclic
parity-check matrices. Based on the observed properties of parity-check
matrices with good stopping redundancy characteristics, we develop a novel
decoding technique, termed automorphism group decoding, that combines iterative
message passing and permutation decoding. We also present bounds on the
smallest number of permutations of an automorphism group decoder needed to
correct any set of erasures up to a prescribed size. Simulation results
demonstrate that for a large number of algebraic codes, the performance of the
new decoding method is close to that of maximum likelihood decoding.Comment: 40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on
Information Theor
Almost Optimal Streaming Algorithms for Coverage Problems
Maximum coverage and minimum set cover problems --collectively called
coverage problems-- have been studied extensively in streaming models. However,
previous research not only achieve sub-optimal approximation factors and space
complexities, but also study a restricted set arrival model which makes an
explicit or implicit assumption on oracle access to the sets, ignoring the
complexity of reading and storing the whole set at once. In this paper, we
address the above shortcomings, and present algorithms with improved
approximation factor and improved space complexity, and prove that our results
are almost tight. Moreover, unlike most of previous work, our results hold on a
more general edge arrival model. More specifically, we present (almost) optimal
approximation algorithms for maximum coverage and minimum set cover problems in
the streaming model with an (almost) optimal space complexity of
, i.e., the space is {\em independent of the size of the sets or
the size of the ground set of elements}. These results not only improve over
the best known algorithms for the set arrival model, but also are the first
such algorithms for the more powerful {\em edge arrival} model. In order to
achieve the above results, we introduce a new general sketching technique for
coverage functions: This sketching scheme can be applied to convert an
-approximation algorithm for a coverage problem to a
(1-\eps)\alpha-approximation algorithm for the same problem in streaming, or
RAM models. We show the significance of our sketching technique by ruling out
the possibility of solving coverage problems via accessing (as a black box) a
(1 \pm \eps)-approximate oracle (e.g., a sketch function) that estimates the
coverage function on any subfamily of the sets
GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra
We propose GraphMineSuite (GMS): the first benchmarking suite for graph
mining that facilitates evaluating and constructing high-performance graph
mining algorithms. First, GMS comes with a benchmark specification based on
extensive literature review, prescribing representative problems, algorithms,
and datasets. Second, GMS offers a carefully designed software platform for
seamless testing of different fine-grained elements of graph mining algorithms,
such as graph representations or algorithm subroutines. The platform includes
parallel implementations of more than 40 considered baselines, and it
facilitates developing complex and fast mining algorithms. High modularity is
possible by harnessing set algebra operations such as set intersection and
difference, which enables breaking complex graph mining algorithms into simple
building blocks that can be separately experimented with. GMS is supported with
a broad concurrency analysis for portability in performance insights, and a
novel performance metric to assess the throughput of graph mining algorithms,
enabling more insightful evaluation. As use cases, we harness GMS to rapidly
redesign and accelerate state-of-the-art baselines of core graph mining
problems: degeneracy reordering (by up to >2x), maximal clique listing (by up
to >9x), k-clique listing (by 1.1x), and subgraph isomorphism (by up to 2.5x),
also obtaining better theoretical performance bounds
Quantum cryptography: key distribution and beyond
Uniquely among the sciences, quantum cryptography has driven both
foundational research as well as practical real-life applications. We review
the progress of quantum cryptography in the last decade, covering quantum key
distribution and other applications.Comment: It's a review on quantum cryptography and it is not restricted to QK
Motif Clustering and Overlapping Clustering for Social Network Analysis
Motivated by applications in social network community analysis, we introduce
a new clustering paradigm termed motif clustering. Unlike classical clustering,
motif clustering aims to minimize the number of clustering errors associated
with both edges and certain higher order graph structures (motifs) that
represent "atomic units" of social organizations. Our contributions are
two-fold: We first introduce motif correlation clustering, in which the goal is
to agnostically partition the vertices of a weighted complete graph so that
certain predetermined "important" social subgraphs mostly lie within the same
cluster, while "less relevant" social subgraphs are allowed to lie across
clusters. We then proceed to introduce the notion of motif covers, in which the
goal is to cover the vertices of motifs via the smallest number of (near)
cliques in the graph. Motif cover algorithms provide a natural solution for
overlapping clustering and they also play an important role in latent feature
inference of networks. For both motif correlation clustering and its extension
introduced via the covering problem, we provide hardness results, algorithmic
solutions and community detection results for two well-studied social networks
Abstracting soft constraints: framework, properties, examples
Soft constraints are very and expressive. However, they also are very complex to handle. For this reason, it may be reasonable in several cases to pass to an abstract version of a given soft constraint problem, and then to bring some useful information from the abstract problem to the concrete one. This will hopefully make the search for a solution, or for an optimal solution, of the concrete problem, faster. In this paper we propose an abstraction scheme for soft constraint problems and we study its main properties. We show that processing the abstracted version of a soft constraint problem can help us in finding good approximations of the optimal solutions, or also in obtaining information that can make the subsequent search for the best solution easier. We also show how the abstraction scheme can be used to devise new hybrid algorithms for solving soft constraint problems, and also to import constraint propagation algorithms from the abstract scenario to the concrete one. This may be useful when we don\u27t have any (or any efficient) propagation algorithm in the concrete setting
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