An O(n^3)-Time Algorithm for Tree Edit Distance

The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case $O(n^3)$-time algorithm for this problem, improving the previous best $O(n^3\log n)$-time algorithm~\cite{Klein}. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems (which is interesting in its own right), together with a deeper understanding of the previous algorithms for the problem. We also prove the optimality of our algorithm among the family of \emph{decomposition strategy} algorithms--which also includes the previous fastest algorithms--by tightening the known lower bound of $\Omega(n^2\log^2 n)$~\cite{Touzet} to $\Omega(n^3)$, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of $\Theta(n m^2 (1 + \log \frac{n}{m}))$ when the two trees have different sizes $m$ and~$n$, where $m < n$.Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on

Edit Distance between Unrooted Trees in Cubic Time

Edit distance between trees is a natural generalization of the classical edit distance between strings, in which the allowed elementary operations are contraction, uncontraction and relabeling of an edge. Demaine et al. [ACM Trans. on Algorithms, 6(1), 2009] showed how to compute the edit distance between rooted trees on n nodes in O(n^3) time. However, generalizing their method to unrooted trees seems quite problematic, and the most efficient known solution remains to be the previous O(n^3 log n) time algorithm by Klein [ESA 1998]. Given the lack of progress on improving this complexity, it might appear that unrooted trees are simply more difficult than rooted trees. We show that this is, in fact, not the case, and edit distance between unrooted trees on n nodes can be computed in O(n^3) time. A significantly faster solution is unlikely to exist, as Bringmann et al. [SODA 2018] proved that the complexity of computing the edit distance between rooted trees cannot be decreased to O(n^{3-epsilon}) unless some popular conjecture fails, and the lower bound easily extends to unrooted trees. We also show that for two unrooted trees of size m and n, where m <=n, our algorithm can be modified to run in O(nm^2(1+log(n/m))). This, again, matches the complexity achieved by Demaine et al. for rooted trees, who also showed that this is optimal if we restrict ourselves to the so-called decomposition algorithms

FixMiner: Mining Relevant Fix Patterns for Automated Program Repair

Patching is a common activity in software development. It is generally performed on a source code base to address bugs or add new functionalities. In this context, given the recurrence of bugs across projects, the associated similar patches can be leveraged to extract generic fix actions. While the literature includes various approaches leveraging similarity among patches to guide program repair, these approaches often do not yield fix patterns that are tractable and reusable as actionable input to APR systems. In this paper, we propose a systematic and automated approach to mining relevant and actionable fix patterns based on an iterative clustering strategy applied to atomic changes within patches. The goal of FixMiner is thus to infer separate and reusable fix patterns that can be leveraged in other patch generation systems. Our technique, FixMiner, leverages Rich Edit Script which is a specialized tree structure of the edit scripts that captures the AST-level context of the code changes. FixMiner uses different tree representations of Rich Edit Scripts for each round of clustering to identify similar changes. These are abstract syntax trees, edit actions trees, and code context trees. We have evaluated FixMiner on thousands of software patches collected from open source projects. Preliminary results show that we are able to mine accurate patterns, efficiently exploiting change information in Rich Edit Scripts. We further integrated the mined patterns to an automated program repair prototype, PARFixMiner, with which we are able to correctly fix 26 bugs of the Defects4J benchmark. Beyond this quantitative performance, we show that the mined fix patterns are sufficiently relevant to produce patches with a high probability of correctness: 81% of PARFixMiner's generated plausible patches are correct.Comment: 31 pages, 11 figure

Automatic document clustering using topic analysis

Web users are demanding more out of current search engines. This can be noticed by the behaviour of users when interacting with search engines [12, 28]. Besides traditional query/results interactions, other tools are springing up on the web. An example of such tools includes web document clustering systems. The idea is for the user to interact with the system by navigating through an organised hierarchy of topics. Document clustering is ideal for unspecified search goals or for the exploration of a topic by the inexpert [21]. Document clustering is there to transform the current interactions of searching through a large amount of links into an efficient interaction where the interaction is navigation through hierarchies. This report will give an overview of the major work in this area, we will also propose our current work, progress and pitfalls which are being tackled.peer-reviewe

TREE-D-SEEK: A Framework for Retrieving Three-Dimensional Scenes

In this dissertation, a strategy and framework for retrieving 3D scenes is proposed. The strategy is to retrieve 3D scenes based on a unified approach for indexing content from disparate information sources and information levels. The TREE-D-SEEK framework implements the proposed strategy for retrieving 3D scenes and is capable of indexing content from a variety of corpora at distinct information levels. A semantic annotation model for indexing 3D scenes in the TREE-D-SEEK framework is also proposed. The semantic annotation model is based on an ontology for rapid prototyping of 3D virtual worlds. With ongoing improvements in computer hardware and 3D technology, the cost associated with the acquisition, production and deployment of 3D scenes is decreasing. As a consequence, there is a need for efficient 3D retrieval systems for the increasing number of 3D scenes in corpora. An efficient 3D retrieval system provides several benefits such as enhanced sharing and reuse of 3D scenes and 3D content. Existing 3D retrieval systems are closed systems and provide search solutions based on a predefined set of indexing and matching algorithms Existing 3D search systems and search solutions cannot be customized for specific requirements, type of information source and information level. In this research, TREE-D-SEEK—an open, extensible framework for retrieving 3D scenes—is proposed. The TREE-D-SEEK framework is capable of retrieving 3D scenes based on indexing low level content to high-level semantic metadata. The TREE-D-SEEK framework is discussed from a software architecture perspective. The architecture is based on a common process flow derived from indexing disparate information sources. Several indexing and matching algorithms are implemented. Experiments are conducted to evaluate the usability and performance of the framework. Retrieval performance of the framework is evaluated using benchmarks and manually collected corpora. A generic, semantic annotation model is proposed for indexing a 3D scene. The primary objective of using the semantic annotation model in the TREE-D-SEEK framework is to improve retrieval relevance and to support richer queries within a 3D scene. The semantic annotation model is driven by an ontology. The ontology is derived from a 3D rapid prototyping framework. The TREE-D-SEEK framework supports querying by example, keyword based and semantic annotation based query types for retrieving 3D scenes