Tree Pattern Matching Research Articles

Forward linearised tree pattern matching using tree pattern border array

We define a tree pattern border array as a property of linearised trees analogous to border arrays from the string domain. We consider tree patterns with node wildcards and subtree wildcards. Then we use the tree pattern border array in a new forward tree pattern matching algorithm for ordered ranked trees. The algorithm finds all occurrences of a single linearised tree pattern in a linearised input tree. As with the classical Morris–Pratt algorithm for searching in strings, the tree pattern border array is used to determine shift lengths in the searching phase of the tree pattern matching algorithm. We compare this new algorithm with the best performing previously existing algorithms based on backward linearised tree pattern matching algorithms, (non-)linearised tree pattern matching algorithms using finite tree automata or stringpath matchers. We show that our new algorithm outperforms other tree pattern matching algorithms in single tree pattern matching.

Source Matching and Rewriting for MLIR Using String-Based Automata

A typical compiler flow relies on a uni-directional sequence of translation/optimization steps that lower the program abstract representation, making it hard to preserve higher-level program information across each transformation step. On the other hand, modern ISA extensions and hardware accelerators can benefit from the compiler’s ability to detect and raise program idioms to acceleration instructions or optimized library calls. Although recent works based on Multi-Level IR (MLIR) have been proposed for code raising, they rely on specialized languages, compiler recompilation, or in-depth dialect knowledge. This article presents Source Matching and Rewriting (SMR), a user-oriented source-code-based approach for MLIR idiom matching and rewriting that does not require a compiler expert’s intervention. SMR uses a two-phase automaton-based DAG-matching algorithm inspired by early work on tree-pattern matching. First, the idiom Control-Dependency Graph (CDG) is matched against the program’s CDG to rule out code fragments that do not have a control-flow structure similar to the desired idiom. Second, candidate code fragments from the previous phase have their Data-Dependency Graphs (DDGs) constructed and matched against the idiom DDG. Experimental results show that SMR can effectively match idioms from Fortran (FIR) and C (CIL) programs while raising them as BLAS calls to improve performance. Additional experiments also show performance improvements when using SMR to enable code replacement in areas like approximate computing and hardware acceleration.

On modification of Boyer-Moore-horspool's algorithm for tree pattern matching in linearised trees

Tree pattern matching on ordered trees is an important problem in Computer Science. Ordered trees can be represented as strings with additional properties via various linearisations. We present a backward tree pattern matching algorithm for ordered trees for various linear representations of trees and tree patterns. The algorithm adaptations find all occurrences of a single given tree pattern which match an input tree regardless of the chosen linearisation. The algorithms preserve the properties and advantages of standard backward string pattern matching using Boyer-Moore-Horspool's bad character shift heuristics. The number of symbol comparisons in the backward tree pattern matching can be sublinear in the size of the input tree. As in the case of the string version of Boyer-Moore-Horspool's matching algorithm, the size of the bad character shift table used by the algorithm is linear in the size of the alphabet. We compare the algorithm adaptations with the algorithm using originally chosen linear representation and with the best performing previously existing algorithms based on (non-linearised) tree pattern matching using finite tree automata or stringpath matchers. We show that the presented backward tree pattern matching algorithms outperform the non-linearising ones for single pattern matching and they perform among themselves comparably.

Simple tree pattern matching for trees in the prefix bar notation

A pushdown automata based algorithm for searching all occurrences of a tree pattern in a rooted directed labelled ordered subject tree is presented. The algorithm allows tree pattern matching with don’t care symbols and with multiple patterns. The subject tree may be for example an abstract syntax tree of a compiler or validating source text editor. Further, a construction and practical evaluation of a simulation algorithm of pushdown automata based tree pattern matching is described.

TPMS: a set of utilities for querying collections of gene trees

BackgroundThe information in large collections of phylogenetic trees is useful for many comparative genomic studies. Therefore, there is a need for flexible tools that allow exploration of such collections in order to retrieve relevant data as quickly as possible.ResultsIn this paper, we present TPMS (Tree Pattern-Matching Suite), a set of programs for handling and retrieving gene trees according to different criteria. The programs from the suite include utilities for tree collection building, specific tree-pattern search strategies and tree rooting. Use of TPMS is illustrated through three examples: systematic search for incongruencies in a large tree collection, a short study on the Coelomata/Ecdysozoa controversy and an evaluation of the level of support for a recently published Mammal phylogeny.ConclusionTPMS is a powerful suite allowing to quickly retrieve sets of trees matching complex patterns in large collection or to root trees using more rigorous approaches than the classical midpoint method. As it is made of a set of command-line programs, it can be easily integrated in any sequence analysis pipeline for an automated use.

Tree template matching in unranked ordered trees

We consider the problem of tree template matching, a type of tree pattern matching, where the tree templates have some of their leaves denoted as “donʼt care”, and propose a solution based on the bottom-up technique. Specifically, we transform the tree pattern matching problem for unranked ordered trees to a string matching problem, by transforming the tree template and the subject tree to strings representing their postfix bar notation, and then propose a table-driven algorithm to solve it. The proposed algorithm is divided into two phases: the preprocessing and the searching phase. The tree template is preprocessed once, and the searching phase can be applied to many subject trees, without the need of preprocessing the tree template again. Although we prove that the space required for preprocessing is exponential in the size of the tree template in the worst case, we show that for a specific class of tree templates, the space required is linear in the size of the tree template. The time for the searching phase is linear in the size of the subject tree in the worst case. Thus, the algorithm is asymptotically optimal when one needs to search for a given tree template, of constant to logarithmic size, in many subject trees.

Automatic generation of compiler backends

Application-specific instruction set processors have proven successful in meeting the various design constraints of modern embedded systems and often provide the only viable trade-off between computing power and opposing metrics such as power consumption. A promising approach to facilitate the exploration of processor design alternatives are processor description languages, which capture the instruction set and hardware organization of a processor. With the use of those processor models, various design tasks, for example, the adaption of software development tools, the generation of hardware models, and various verification tasks, can be automatized. These languages thus allow effective shortening of development turnaround times. In this work, the novel xADL language is presented, which, in contrast to most contemporary processor description languages, focuses on a structural modeling of the processor's hardware organization. However, a behavioral model of the instruction set is automatically derived using instruction set extraction. This provides a tight coupling between the structural hardware view and the instruction set view of the processor and reduces the complexity of processor models in comparison with existing languages. The feasibility of our approach is demonstrated by a compiler backend generator based on tree pattern matching. An important property of our generator is its ability to automatically verify whether the resulting compiler is complete, that is, it can process all possible input programs. The generated compilers are competitive to handcrafted production compilers, showing speedups of up to 20% for certain benchmarks. On average, moderate slowdowns between 3% and 15% have been observed for several processor models while considerable reductions in code size have been measured. Copyright © 2012 John Wiley & Sons, Ltd.

Indexing ordered trees for (nonlinear) tree pattern matching by pushdown automata

Trees are one of the fundamental data structures used in Computer Science. We present a new kind of acyclic pushdown automata, the tree pattern pushdown automaton and the nonlinear tree pattern pushdown automaton, constructed for an ordered tree. These automata accept all tree patterns and nonlinear tree patterns, respectively, which match the tree and represent a full index of the tree for such patterns. Given a tree with n nodes, the numbers of these distinct tree patterns and nonlinear tree patterns can be at most 2n?1 +n and at most (2+v)n?1+2, respectively, where v is the maximal number of nonlinear variables allowed in nonlinear tree patterns. The total sizes of nondeterministic versions of the two pushdown automata are O(n) and O(n2), respectively. We discuss the time complexities and show timings of our implementations using the bit-parallelism technique. The timings show that for a given tree the running time is linear to the size of the input pattern.

Efficiency of TreeMatch Algorithm in XML Tree Pattern Matching

In Recent days exchange XML data more often in organizations and business sectors, so there is an increasing need for effective and efficient processing of queries on XML data. This paper presents a wide analysis to identify the efficiency of XML tree pattern matching algorithms. Previous years many methods have been proposed to match XML tree queries efficiently. In particularly TwigStack, OrderedTJ, TJFast and TreeMatch algorithms. All algorithms to achieve something through these own ways like structural relationship including Parent - Child (P-C) relationship (denoted as '/') and Ancestor-Descendent (A-D) relationships (denoted as '//') and more. Finally, we report our results to show that which algorithm is superior to previous approaches in terms of the performance. Keywords - Efficient TPQ, Efficiency of Tree pattern, XML Tree pattern

A Survey of XML Tree Patterns

With XML becoming a ubiquitous language for data interoperability purposes in various domains, efficiently querying XML data is a critical issue. This has lead to the design of algebraic frameworks based on tree-shaped patterns akin to the tree-structured data model of XML. Tree patterns are graphic representations of queries over data trees. They are actually matched against an input data tree to answer a query. Since the turn of the 21st century, an astounding research effort has been focusing on tree pattern models and matching optimization (a primordial issue). This paper is a comprehensive survey of these topics, in which we outline and compare the various features of tree patterns. We also review and discuss the two main families of approaches for optimizing tree pattern matching, namely pattern tree minimization and holistic matching. We finally present actual tree pattern-based developments, to provide a global overview of this significant research topic.

Extended XML Tree Pattern Matching: Theories and Algorithms

As business and enterprises generate and exchange XML data more often, there is an increasing need for efficient processing of queries on XML data. Searching for the occurrences of a tree pattern query in an XML database is a core operation in XML query processing. Prior works demonstrate that holistic twig pattern matching algorithm is an efficient technique to answer an XML tree pattern with parent-child (P-C) and ancestor-descendant (A-D) relationships, as it can effectively control the size of intermediate results during query processing. However, XML query languages (e.g., XPath and XQuery) define more axes and functions such as negation function, order-based axis, and wildcards. In this paper, we research a large set of XML tree pattern, called extended XML tree pattern, which may include P-C, A-D relationships, negation functions, wildcards, and order restriction. We establish a theoretical framework about “matching cross” which demonstrates the intrinsic reason in the proof of optimality on holistic algorithms. Based on our theorems, we propose a set of novel algorithms to efficiently process three categories of extended XML tree patterns. A set of experimental results on both real-life and synthetic data sets demonstrate the effectiveness and efficiency of our proposed theories and algorithms.

Rigid tree automata and applications

We introduce the class of rigid tree automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, non-linear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NP-complete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. This result, one of the first on rewrite closure of languages of tree automata with constraints, is enabling the extension of model checking procedures based on finite tree automata techniques, in particular for the verification of communicating processes with several local non-rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided.

Indexing and querying XML using extended Dewey labeling scheme

Finding all the occurrences of a tree pattern in an XML database is a core operation for efficient evaluation of XML queries. The Dewey labeling scheme is commonly used to label an XML document to facilitate XML query processing by recording information on the path of an element. In order to improve the efficiency of XML tree pattern matching, we introduce a novel labeling scheme, called extended Dewey, which effectively extends the existing Dewey labeling scheme to combine the types and identifiers of elements in a label, and to avoid the scan of labels for internal query nodes to accelerate query processing (in I/O cost). Based on extended Dewey, we propose a series of holistic XML tree pattern matching algorithms. We first present TJFast to answer an XML twig pattern query. To efficiently answer a generalized XML tree pattern, we then propose GTJFast, an optimization that exploits the non-output nodes. In addition, we propose TJFastTL and GTJFastTL based on the tag + level data partition scheme to further reduce I/O costs by level pruning. Finally, we report our comprehensive experimental results to show that our set of XML tree pattern matching algorithms are superior to existing approaches in terms of the number of elements scanned, the size of intermediate results and query performance.

Principles of Holism for sequential twig pattern matching

Modern applications face the challenge of dealing with structured and semi-structured data. They have to deal with complex objects, most of them presenting some kind of internal structure, which often forms a hierarchy. Though XML documents are the most known, chemical compounds, CAD drawings, web-sites and many other applications have to deal with similar problems. In such environments, ordered and unordered tree pattern matching are the fundamental search operations. One of the main thrusts of research activities for tree pattern matching is the class of holistic approaches. Their ultimate goal is to evaluate a query twig as a whole by relying on sequential access patterns and non trivial auxiliary storage structures, typically stored in main memory. Based on the pre/post-order ranks of individual tree nodes, we establish strong theoretical bases as a foundation for correct and efficient holistic pattern matching algorithms. In particular, we define and prove sufficient and necessary conditions to minimize the amount of data retained in memory, thus introducing a correct and complete framework on which different holistic solutions can be compared. We also show how these rules can be applied for building algorithms for ordered and unordered tree-pattern matching. Thanks to the above theoretical achievements, each holistic algorithm gains in efficiency as it is directly implemented on the adopted numbering scheme, avoids expensive matching refinements and keeps memory requirements stable. An experimental analysis and comparison with previous approaches confirms the superiority of our approach tested on synthetic as well as real-life data sets.

Efficient algorithms for descendant-only tree pattern queries

Tree pattern matching is a fundamental problem that has a wide range of applications in Web data management, XML processing, and selective data dissemination. In this paper we develop efficient algorithms for the tree homeomorphism problem, i.e., the problem of matching a tree pattern with exclusively transitive (descendant) edges. We first prove that deciding whether there is a tree homeomorphism is LOGSPACE-complete, improving on the current LOGCFL upper bound. Furthermore, we develop a practical algorithm for the tree homeomorphism decision problem that is both space- and time-efficient. The algorithm is in LOGDCFL and space consumption is strongly bounded, while the running time is linear in the size of the data tree. This algorithm immediately generalizes to the problem of matching the tree pattern against all subtrees of the data tree, preserving the mentioned efficiency properties.

On Tree Pattern Matching by Pushdown Automata

Tree pattern matching is an important operation in Computer Science on which a number of tasks such as mechanical theorem proving, term-rewriting, symbolic computation and non-procedural programming languages are based on. Work has begun on a systematic approach to the construction of tree pattern matchers by deterministic pushdown automata which read subject trees in prefix notation. The method is analogous to the construction of string pattern matchers: for given patterns, a non-deterministic pushdown automaton is created and then it is determinised. In this first paper, we present the proposed non-deterministic pushdown automaton which will serve as a basis for the determinisation process, and prove its correctness.

Path Summaries and Path Partitioning in Modern XML Databases

XML path summaries are compact structures representing all the simple parent-child paths of an XML document. Such paths have also been used in many works as a basis for partitioning the document’s content in a persistent store, under the form of path indices or path tables. We revisit the notions of path summaries and path-driven storage model in the context of current-day XML databases. This context is characterized by complex queries, typically expressed in an XQuery subset, and by the presence of efficient encoding techniques such as structural node identifiers. We review a path summary’s many uses for query optimization, and given them a common basis, namely relevant paths. We discuss summary-based tree pattern minimization and present some efficient summary-based minimization heuristics. We consider relevant path computation and provide a time- and memory-efficient computation algorithm. We combine the principle of path partitioning with the presence of structural identifiers in a simple path-partitioned storage model, which allows for selective data access and efficient query plans. This model improves the efficiency of twig query processing up to two orders of magnitude over the similar tag-partitioned indexing model. We have implemented the path-partitioned storage model and path summaries in the XQueC compressed database prototype [8]. We present an experimental evaluation of a path summary’s practical feasibility and of tree pattern matching in a path-partitioned store.

TWO RELATED ALGORITHMS FOR ROOT-TO-FRONTIER TREE PATTERN MATCHING

Tree pattern matching (TPM) algorithms on ordered, ranked trees play an important role in applications such as compilers and term rewriting systems. Many TPM algorithms appearing in the literature are based on tree automata. For efficiency, these automata should be deterministic, yet deterministic root-to-frontier tree automata (DRFTAS) are less powerful than nondeterministic ones, and no root-to-frontier TPM algorithm using a DRFTA has appeared so far. Hoffmann & O'Donnell presented a root-to-frontier TPM algorithm based on an Aho-Corasick automaton recognizing tree stringpaths. No relationship between this algorithm and algorithms using tree automata has however been described. We show that a specific DRFTA can be used for stringpath matching in a root-to-frontier TPM algorithm. This new algorithm provides a missing link between TPM algorithms using stringpath automata and those using tree automata. We also investigate the correspondence between the automata used by the two algorithms.

An algebraic view of the relation between largest common subtrees and smallest common supertrees

The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree problems, is established by means of simple constructions, which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them, and vice versa. These constructions are the same for isomorphic, homeomorphic, topological, and minor embeddings, they take only time linear in the size of the trees, and they turn out to have a clear algebraic meaning.

Tree pattern matching in phylogenetic trees: automatic search for orthologs or paralogs in homologous gene sequence databases

Comparative sequence analysis is widely used to study genome function and evolution. This approach first requires the identification of homologous genes and then the interpretation of their homology relationships (orthology or paralogy). To provide help in this complex task, we developed three databases of homologous genes containing sequences, multiple alignments and phylogenetic trees: HOBACGEN, HOVERGEN and HOGENOM. In this paper, we present two new tools for automating the search for orthologs or paralogs in these databases. First, we have developed and implemented an algorithm to infer speciation and duplication events by comparison of gene and species trees (tree reconciliation). Second, we have developed a general method to search in our databases the gene families for which the tree topology matches a peculiar tree pattern. This algorithm of unordered tree pattern matching has been implemented in the FamFetch graphical interface. With the help of a graphical editor, the user can specify the topology of the tree pattern, and set constraints on its nodes and leaves. Then, this pattern is compared with all the phylogenetic trees of the database, to retrieve the families in which one or several occurrences of this pattern are found. By specifying ad hoc patterns, it is therefore possible to identify orthologs in our databases.