Incremental construction of minimal acyclic finite-state automata

In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it. Our approach is to construct a minimal automaton in a single phase by adding new strings one by one and minimizing the resulting automaton on-the-fly. We present a general algorithm as well as a specialization that relies upon the lexicographical ordering of the input strings.Comment: 14 pages, 7 figure

Distributed PCP Theorems for Hardness of Approximation in P

We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying assignment $x \in \{0,1\}^n$ to a CNF formula $\varphi$ is shared between two parties, where Alice knows $x_1, \dots, x_{n/2}$, Bob knows $x_{n/2+1},\dots,x_n$, and both parties know $\varphi$. The goal is to have Alice and Bob jointly write a PCP that $x$ satisfies $\varphi$, while exchanging little or no information. Unfortunately, this model as-is does not allow for nontrivial query complexity. Instead, we focus on a non-deterministic variant, where the players are helped by Merlin, a third party who knows all of $x$. Using our framework, we obtain, for the first time, PCP-like reductions from the Strong Exponential Time Hypothesis (SETH) to approximation problems in P. In particular, under SETH we show that there are no truly-subquadratic approximation algorithms for Bichromatic Maximum Inner Product over {0,1}-vectors, Bichromatic LCS Closest Pair over permutations, Approximate Regular Expression Matching, and Diameter in Product Metric. All our inapproximability factors are nearly-tight. In particular, for the first two problems we obtain nearly-polynomial factors of $2^{(\log n)^{1-o(1)}}$; only $(1+o(1))$-factor lower bounds (under SETH) were known before

Syntax tree fingerprinting: a foundation for source code similarity detection

Plagiarism detection and clone refactoring in software depend on one common concern: nding similar source chunks across large repositories. However, since code duplication in software is often the result of copy-paste behaviors, only minor modi cations are expected between shared codes. On the contrary, in a plagiarism detection context, edits are more extensive and exact matching strategies show their limits. Among the three main representations used by source code similarity detection tools, namely the linear token sequences, the Abstract Syntax Tree (AST) and the Program Depen- dency Graph (PDG), we believe that the AST could e ciently support the program analysis and transformations required for the advanced similarity detection process. In this paper we present a simple and scalable architecture based on syntax tree nger- printing. Thanks to a study of several hashing strategies reducing false-positive collisions, we propose a framework that e ciently indexes AST representations in a database, that quickly detects exact (w.r.t source code abstraction) clone clusters and that easily retrieves their corresponding ASTs. Our aim is to allow further processing of neighboring exact matches in order to identify the larger approximate matches, dealing with the common modi cation patterns seen in the intra-project copy-pastes and in the plagiarism cases

Scalable RDF Data Compression using X10

The Semantic Web comprises enormous volumes of semi-structured data elements. For interoperability, these elements are represented by long strings. Such representations are not efficient for the purposes of Semantic Web applications that perform computations over large volumes of information. A typical method for alleviating the impact of this problem is through the use of compression methods that produce more compact representations of the data. The use of dictionary encoding for this purpose is particularly prevalent in Semantic Web database systems. However, centralized implementations present performance bottlenecks, giving rise to the need for scalable, efficient distributed encoding schemes. In this paper, we describe an encoding implementation based on the asynchronous partitioned global address space (APGAS) parallel programming model. We evaluate performance on a cluster of up to 384 cores and datasets of up to 11 billion triples (1.9 TB). Compared to the state-of-art MapReduce algorithm, we demonstrate a speedup of 2.6-7.4x and excellent scalability. These results illustrate the strong potential of the APGAS model for efficient implementation of dictionary encoding and contributes to the engineering of larger scale Semantic Web applications

Efficient String Graph Construction Algorithm

In the field of genome assembly research where assemblers are dominated by de Bruijn graph-based approaches, string graph-based assembly approach is getting more attention because of its ability to losslessly retain information from sequence data. Despite the advantages provided by a string graph in repeat detection and in maintaining read coherence, the high computational cost for constructing a string graph hinders its usability for genome assembly. Even though different algorithms have been proposed over the last decade for string graph construction, efficiency is still a challenge due to the demand for processing a large amount of sequence data generated by NGS technologies. Therefore, in this thesis, we provide a novel, linear time and alphabet-size-independent algorithm SOF which uses the property of irreducible edges and transitive edges to efficiently construct string graph from an overlap graph. Experimental results show that SOF is at least 2 times faster than the string graph construction algorithm provided in SGA, one of the most popular string graph-based assembler, while maintaining almost the same memory footprint as SGA. Moreover, the availability of SOF as a subprogram in the SGA assembly pipeline will give user facilities to access the preprocessing and postprocessing steps for genome assembly provided in SGA