Introduction to Algorithms
01 Jan 2005-
About: The article was published on 2005-01-01 and is currently open access. It has received 19250 citations till now. The article focuses on the topics: Internal sort.
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TL;DR: It is demonstrated that the algorithms proposed are highly effective at discovering community structure in both computer-generated and real-world network data, and can be used to shed light on the sometimes dauntingly complex structure of networked systems.
Abstract: We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.
12,882 citations
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
9,441 citations
Proceedings Article•
25 Jul 2004TL;DR: Four different RouGE measures are introduced: ROUGE-N, ROUge-L, R OUGE-W, and ROUAGE-S included in the Rouge summarization evaluation package and their evaluations.
Abstract: ROUGE stands for Recall-Oriented Understudy for Gisting Evaluation. It includes measures to automatically determine the quality of a summary by comparing it to other (ideal) summaries created by humans. The measures count the number of overlapping units such as n-gram, word sequences, and word pairs between the computer-generated summary to be evaluated and the ideal summaries created by humans. This paper introduces four different ROUGE measures: ROUGE-N, ROUGE-L, ROUGE-W, and ROUGE-S included in the ROUGE summarization evaluation package and their evaluations. Three of them have been used in the Document Understanding Conference (DUC) 2004, a large-scale summarization evaluation sponsored by NIST.
9,293 citations
TL;DR: It appears that the 5′ and 3′ UTRs are reservoirs for genetic variations that changes the termini of proteins during evolution of the Drosophila genus.
Abstract: We describe a new computer program, SnpEff, for rapidly categorizing the effects of variants in genome sequences. Once a genome is sequenced, SnpEff annotates variants based on their genomic locations and predicts coding effects. Annotated genomic locations include intronic, untranslated region, upstream, downstream, splice site, or intergenic regions. Coding effects such as synonymous or non-synonymous amino acid replacement, start codon gains or losses, stop codon gains or losses, or frame shifts can be predicted. Here the use of SnpEff is illustrated by annotating ~356,660 candidate SNPs in ~117 Mb unique sequences, representing a substitution rate of ~1/305 nucleotides, between the Drosophila melanogaster w1118; iso-2; iso-3 strain and the reference y1; cn1 bw1 sp1 strain. We show that ~15,842 SNPs are synonymous and ~4,467 SNPs are non-synonymous (N/S ~0.28). The remaining SNPs are in other categories, such as stop codon gains (38 SNPs), stop codon losses (8 SNPs), and start codon gains (297 SNPs) in...
8,017 citations
TL;DR: A hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure.
Abstract: The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m approximately n and d approximately log n, in which case our algorithm runs in essentially linear time, O (n log(2) n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on-line retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 x 10(6) edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.
6,599 citations