2,400 research outputs found
Edit Distance: Sketching, Streaming and Document Exchange
We show that in the document exchange problem, where Alice holds and Bob holds , Alice can send Bob a message of
size bits such that Bob can recover using the
message and his input if the edit distance between and is no more
than , and output "error" otherwise. Both the encoding and decoding can be
done in time . This result significantly
improves the previous communication bounds under polynomial encoding/decoding
time. We also show that in the referee model, where Alice and Bob hold and
respectively, they can compute sketches of and of sizes
bits (the encoding), and send to the referee, who can
then compute the edit distance between and together with all the edit
operations if the edit distance is no more than , and output "error"
otherwise (the decoding). To the best of our knowledge, this is the first
result for sketching edit distance using bits.
Moreover, the encoding phase of our sketching algorithm can be performed by
scanning the input string in one pass. Thus our sketching algorithm also
implies the first streaming algorithm for computing edit distance and all the
edits exactly using bits of space.Comment: Full version of an article to be presented at the 57th Annual IEEE
Symposium on Foundations of Computer Science (FOCS 2016
Graph edit distance from spectral seriation
This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems
On the Effect of Semantically Enriched Context Models on Software Modularization
Many of the existing approaches for program comprehension rely on the
linguistic information found in source code, such as identifier names and
comments. Semantic clustering is one such technique for modularization of the
system that relies on the informal semantics of the program, encoded in the
vocabulary used in the source code. Treating the source code as a collection of
tokens loses the semantic information embedded within the identifiers. We try
to overcome this problem by introducing context models for source code
identifiers to obtain a semantic kernel, which can be used for both deriving
the topics that run through the system as well as their clustering. In the
first model, we abstract an identifier to its type representation and build on
this notion of context to construct contextual vector representation of the
source code. The second notion of context is defined based on the flow of data
between identifiers to represent a module as a dependency graph where the nodes
correspond to identifiers and the edges represent the data dependencies between
pairs of identifiers. We have applied our approach to 10 medium-sized open
source Java projects, and show that by introducing contexts for identifiers,
the quality of the modularization of the software systems is improved. Both of
the context models give results that are superior to the plain vector
representation of documents. In some cases, the authoritativeness of
decompositions is improved by 67%. Furthermore, a more detailed evaluation of
our approach on JEdit, an open source editor, demonstrates that inferred topics
through performing topic analysis on the contextual representations are more
meaningful compared to the plain representation of the documents. The proposed
approach in introducing a context model for source code identifiers paves the
way for building tools that support developers in program comprehension tasks
such as application and domain concept location, software modularization and
topic analysis
High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
We consider the problem of high-dimensional Gaussian graphical model
selection. We identify a set of graphs for which an efficient estimation
algorithm exists, and this algorithm is based on thresholding of empirical
conditional covariances. Under a set of transparent conditions, we establish
structural consistency (or sparsistency) for the proposed algorithm, when the
number of samples n=omega(J_{min}^{-2} log p), where p is the number of
variables and J_{min} is the minimum (absolute) edge potential of the graphical
model. The sufficient conditions for sparsistency are based on the notion of
walk-summability of the model and the presence of sparse local vertex
separators in the underlying graph. We also derive novel non-asymptotic
necessary conditions on the number of samples required for sparsistency
Approximate Similarity Search Under Edit Distance Using Locality-Sensitive Hashing
Edit distance similarity search, also called approximate pattern matching, is a fundamental problem with widespread database applications. The goal of the problem is to preprocess n strings of length d, to quickly answer queries q of the form: if there is a database string within edit distance r of q, return a database string within edit distance cr of q.
Previous approaches to this problem either rely on very large (superconstant) approximation ratios c, or very small search radii r. Outside of a narrow parameter range, these solutions are not competitive with trivially searching through all n strings.
In this work we give a simple and easy-to-implement hash function that can quickly answer queries for a wide range of parameters. Specifically, our strategy can answer queries in time O?(d3^rn^{1/c}). The best known practical results require c ? r to achieve any correctness guarantee; meanwhile, the best known theoretical results are very involved and difficult to implement, and require query time that can be loosely bounded below by 24^r. Our results significantly broaden the range of parameters for which there exist nontrivial theoretical bounds, while retaining the practicality of a locality-sensitive hash function
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