GraphFind: enhancing graph searching by low support data mining techniques

<p>Abstract</p> <p>Background</p> <p>Biomedical and chemical databases are large and rapidly growing in size. Graphs naturally model such kinds of data. To fully exploit the wealth of information in these graph databases, a key role is played by systems that search for all exact or approximate occurrences of a query graph. To deal efficiently with graph searching, advanced methods for indexing, representation and matching of graphs have been proposed.</p> <p>Results</p> <p>This paper presents GraphFind. The system implements efficient graph searching algorithms together with advanced filtering techniques that allow approximate search. It allows users to select candidate subgraphs rather than entire graphs. It implements an effective data storage based also on low-support data mining.</p> <p>Conclusions</p> <p>GraphFind is compared with Frowns, GraphGrep and gIndex. Experiments show that GraphFind outperforms the compared systems on a very large collection of small graphs. The proposed low-support mining technique which applies to any searching system also allows a significant index space reduction.</p

A subgraph isomorphism algorithm and its application to biochemical data

BackgroundGraphs can represent biological networks at the molecular, protein, or species level. An important query is to find all matches of a pattern graph to a target graph. Accomplishing this is inherently difficult (NP-complete) and the efficiency of heuristic algorithms for the problem may depend upon the input graphs. The common aim of existing algorithms is to eliminate unsuccessful mappings as early as and as inexpensively as possible.ResultsWe propose a new subgraph isomorphism algorithm which applies a search strategy to significantly reduce the search space without using any complex pruning rules or domain reduction procedures. We compare our method with the most recent and efficient subgraph isomorphism algorithms (VFlib, LAD, and our C++ implementation of FocusSearch which was originally distributed in Modula2) on synthetic, molecules, and interaction networks data. We show a significant reduction in the running time of our approach compared with these other excellent methods and show that our algorithm scales well as memory demands increase.ConclusionsSubgraph isomorphism algorithms are intensively used by biochemical tools. Our analysis gives a comprehensive comparison of different software approaches to subgraph isomorphism highlighting their weaknesses and strengths. This will help researchers make a rational choice among methods depending on their application. We also distribute an open-source package including our system and our own C++ implementation of FocusSearch together with all the used datasets (http://ferrolab.dmi.unict.it/ri.html). In future work, our findings may be extended to approximate subgraph isomorphism algorithms

Algorithms for sparse convolution and sublinear edit distance

In this PhD thesis on fine-grained algorithm design and complexity, we investigate output-sensitive and sublinear-time algorithms for two important problems. (1) Sparse Convolution: Computing the convolution of two vectors is a basic algorithmic primitive with applications across all of Computer Science and Engineering. In the sparse convolution problem we assume that the input and output vectors have at most t nonzero entries, and the goal is to design algorithms with running times dependent on t. For the special case where all entries are nonnegative, which is particularly important for algorithm design, it is known since twenty years that sparse convolutions can be computed in near-linear randomized time O(t log^2 n). In this thesis we develop a randomized algorithm with running time O(t \log t) which is optimal (under some mild assumptions), and the first near-linear deterministic algorithm for sparse nonnegative convolution. We also present an application of these results, leading to seemingly unrelated fine-grained lower bounds against distance oracles in graphs. (2) Sublinear Edit Distance: The edit distance of two strings is a well-studied similarity measure with numerous applications in computational biology. While computing the edit distance exactly provably requires quadratic time, a long line of research has lead to a constant-factor approximation algorithm in almost-linear time. Perhaps surprisingly, it is also possible to approximate the edit distance k within a large factor O(k) in sublinear time O~(n/k + poly(k)). We drastically improve the approximation factor of the known sublinear algorithms from O(k) to k^{o(1)} while preserving the O(n/k + poly(k)) running time.In dieser Doktorarbeit über feinkörnige Algorithmen und Komplexität untersuchen wir ausgabesensitive Algorithmen und Algorithmen mit sublinearer Lauf-zeit für zwei wichtige Probleme. (1) Dünne Faltungen: Die Berechnung der Faltung zweier Vektoren ist ein grundlegendes algorithmisches Primitiv, das in allen Bereichen der Informatik und des Ingenieurwesens Anwendung findet. Für das dünne Faltungsproblem nehmen wir an, dass die Eingabe- und Ausgabevektoren höchstens t Einträge ungleich Null haben, und das Ziel ist, Algorithmen mit Laufzeiten in Abhängigkeit von t zu entwickeln. Für den speziellen Fall, dass alle Einträge nicht-negativ sind, was insbesondere für den Entwurf von Algorithmen relevant ist, ist seit zwanzig Jahren bekannt, dass dünn besetzte Faltungen in nahezu linearer randomisierter Zeit O(t \log^2 n) berechnet werden können. In dieser Arbeit entwickeln wir einen randomisierten Algorithmus mit Laufzeit O(t \log t), der (unter milden Annahmen) optimal ist, und den ersten nahezu linearen deterministischen Algorithmus für dünne nichtnegative Faltungen. Wir stellen auch eine Anwendung dieser Ergebnisse vor, die zu scheinbar unverwandten feinkörnigen unteren Schranken gegen Distanzorakel in Graphen führt. (2) Sublineare Editierdistanz: Die Editierdistanz zweier Zeichenketten ist ein gut untersuchtes Ähnlichkeitsmaß mit zahlreichen Anwendungen in der Computerbiologie. Während die exakte Berechnung der Editierdistanz nachweislich quadratische Zeit erfordert, hat eine lange Reihe von Forschungsarbeiten zu einem Approximationsalgorithmus mit konstantem Faktor in fast-linearer Zeit geführt. Überraschenderweise ist es auch möglich, die Editierdistanz k innerhalb eines großen Faktors O(k) in sublinearer Zeit O~(n/k + poly(k)) zu approximieren. Wir verbessern drastisch den Approximationsfaktor der bekannten sublinearen Algorithmen von O(k) auf k^{o(1)} unter Beibehaltung der O(n/k + poly(k))-Laufzeit