4,019 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
Metrics for Graph Comparison: A Practitioner's Guide
Comparison of graph structure is a ubiquitous task in data analysis and
machine learning, with diverse applications in fields such as neuroscience,
cyber security, social network analysis, and bioinformatics, among others.
Discovery and comparison of structures such as modular communities, rich clubs,
hubs, and trees in data in these fields yields insight into the generative
mechanisms and functional properties of the graph.
Often, two graphs are compared via a pairwise distance measure, with a small
distance indicating structural similarity and vice versa. Common choices
include spectral distances (also known as distances) and distances
based on node affinities. However, there has of yet been no comparative study
of the efficacy of these distance measures in discerning between common graph
topologies and different structural scales.
In this work, we compare commonly used graph metrics and distance measures,
and demonstrate their ability to discern between common topological features
found in both random graph models and empirical datasets. We put forward a
multi-scale picture of graph structure, in which the effect of global and local
structure upon the distance measures is considered. We make recommendations on
the applicability of different distance measures to empirical graph data
problem based on this multi-scale view. Finally, we introduce the Python
library NetComp which implements the graph distances used in this work
High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs
We present a new method for synthesizing high-resolution photo-realistic
images from semantic label maps using conditional generative adversarial
networks (conditional GANs). Conditional GANs have enabled a variety of
applications, but the results are often limited to low-resolution and still far
from realistic. In this work, we generate 2048x1024 visually appealing results
with a novel adversarial loss, as well as new multi-scale generator and
discriminator architectures. Furthermore, we extend our framework to
interactive visual manipulation with two additional features. First, we
incorporate object instance segmentation information, which enables object
manipulations such as removing/adding objects and changing the object category.
Second, we propose a method to generate diverse results given the same input,
allowing users to edit the object appearance interactively. Human opinion
studies demonstrate that our method significantly outperforms existing methods,
advancing both the quality and the resolution of deep image synthesis and
editing.Comment: v2: CVPR camera ready, adding more results for edge-to-photo example
Ontology alignment based on word embedding and random forest classification.
Ontology alignment is crucial for integrating heterogeneous data sources and forms an important component for realising the goals of the semantic web. Accordingly, several ontology alignment techniques have been proposed and used for discovering correspondences between the concepts (or entities) of different ontologies. However, these techniques mostly depend on string-based similarities which are unable to handle the vocabulary mismatch problem. Also, determining which similarity measures to use and how to effectively combine them in alignment systems are challenges that have persisted in this area. In this work, we introduce a random forest classifier approach for ontology alignment which relies on word embedding to discover semantic similarities between concepts. Specifically, we combine string-based and semantic similarity measures to form feature vectors that are used by the classifier model to determine when concepts match. By harnessing background knowledge and relying on minimal information from the ontologies, our approach can deal with knowledge-light ontological resources. It also eliminates the need for learning the aggregation weights of multiple similarity measures. Our experiments using Ontology Alignment Evaluation Initiative (OAEI) dataset and real-world ontologies highlight the utility of our approach and show that it can outperform state-of-the-art alignment systems
The Tree Inclusion Problem: In Linear Space and Faster
Given two rooted, ordered, and labeled trees and the tree inclusion
problem is to determine if can be obtained from by deleting nodes in
. This problem has recently been recognized as an important query primitive
in XML databases. Kilpel\"ainen and Mannila [\emph{SIAM J. Comput. 1995}]
presented the first polynomial time algorithm using quadratic time and space.
Since then several improved results have been obtained for special cases when
and have a small number of leaves or small depth. However, in the worst
case these algorithms still use quadratic time and space. Let , , and
denote the number of nodes, the number of leaves, and the %maximum depth
of a tree . In this paper we show that the tree inclusion
problem can be solved in space and time: O(\min(l_Pn_T, l_Pl_T\log
\log n_T + n_T, \frac{n_Pn_T}{\log n_T} + n_{T}\log n_{T})). This improves or
matches the best known time complexities while using only linear space instead
of quadratic. This is particularly important in practical applications, such as
XML databases, where the space is likely to be a bottleneck.Comment: Minor updates from last tim
Matching XML schemas by a new tree matching algorithm.
Schema matching is one of the key operations in XML-based information integration and exchanging applications. Automatically or semi-automatically matching XML schemas has attracted a lot of attentions in academia and industry due to the extensive adoption of XML techniques. One of the most difficult tasks in this problem is to identify structural relations between two XML schemas. This thesis builds an automatic XML schema matching system which generates two types of outputs: the element mappings and schema similarity. In this system, an XML schema is modeled as a tree. We have proposed a new tree matching algorithm to compute the structural relation by extracting the most similar common substructures. The algorithm has been designed to achieve a trade-off between matching optimality and time complexity. The experimental results show that this system can be used to match large XML schemas.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .W366. Source: Masters Abstracts International, Volume: 43-05, page: 1758. Adviser: Jianguo Lu. Thesis (M.Sc.)--University of Windsor (Canada), 2004
Matching hierarchical structures for shape recognition
In this thesis we aim to develop a framework for clustering trees and rep- resenting and learning a generative model of graph structures from a set of training samples. The approach is applied to the problem of the recognition and classification of shape abstracted in terms of its morphological skeleton. We make five contributions. The first is an algorithm to approximate tree edit-distance using relaxation labeling. The second is the introduction of the tree union, a representation capable of representing the modes of structural variation present in a set of trees. The third is an information theoretic approach to learning a generative model of tree structures from a training set.
While the skeletal abstraction of shape was chosen mainly as a exper- imental vehicle, we, nonetheless, make some contributions to the fields of skeleton extraction and its graph representation. In particular, our fourth contribution is the development of a skeletonization method that corrects curvature effects in the Hamilton-Jacobi framework, improving its localiza- tion and noise sensitivity. Finally, we propose a shape-measure capable of characterizing shapes abstracted in terms of their skeleton. This measure has a number of interesting properties. In particular, it varies smoothly as the shape is deformed and can be easily computed using the presented skeleton extraction algorithm.
Each chapter presents an experimental analysis of the proposed approaches applied to shape recognition problems
Fine-Grained Complexity Analysis of Two Classic TSP Variants
We analyze two classic variants of the Traveling Salesman Problem using the
toolkit of fine-grained complexity. Our first set of results is motivated by
the Bitonic TSP problem: given a set of points in the plane, compute a
shortest tour consisting of two monotone chains. It is a classic
dynamic-programming exercise to solve this problem in time. While the
near-quadratic dependency of similar dynamic programs for Longest Common
Subsequence and Discrete Frechet Distance has recently been proven to be
essentially optimal under the Strong Exponential Time Hypothesis, we show that
bitonic tours can be found in subquadratic time. More precisely, we present an
algorithm that solves bitonic TSP in time and its bottleneck
version in time. Our second set of results concerns the popular
-OPT heuristic for TSP in the graph setting. More precisely, we study the
-OPT decision problem, which asks whether a given tour can be improved by a
-OPT move that replaces edges in the tour by new edges. A simple
algorithm solves -OPT in time for fixed . For 2-OPT, this is
easily seen to be optimal. For we prove that an algorithm with a runtime
of the form exists if and only if All-Pairs
Shortest Paths in weighted digraphs has such an algorithm. The results for
may suggest that the actual time complexity of -OPT is
. We show that this is not the case, by presenting an algorithm
that finds the best -move in time for
fixed . This implies that 4-OPT can be solved in time,
matching the best-known algorithm for 3-OPT. Finally, we show how to beat the
quadratic barrier for in two important settings, namely for points in the
plane and when we want to solve 2-OPT repeatedly.Comment: Extended abstract appears in the Proceedings of the 43rd
International Colloquium on Automata, Languages, and Programming (ICALP 2016
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