Platform Dependent Verification: On Engineering Verification Tools for 21st Century

The paper overviews recent developments in platform-dependent explicit-state LTL model checking.Comment: In Proceedings PDMC 2011, arXiv:1111.006

I/O efficient bisimulation partitioning on very large directed acyclic graphs

In this paper we introduce the first efficient external-memory algorithm to compute the bisimilarity equivalence classes of a directed acyclic graph (DAG). DAGs are commonly used to model data in a wide variety of practical applications, ranging from XML documents and data provenance models, to web taxonomies and scientific workflows. In the study of efficient reasoning over massive graphs, the notion of node bisimilarity plays a central role. For example, grouping together bisimilar nodes in an XML data set is the first step in many sophisticated approaches to building indexing data structures for efficient XPath query evaluation. To date, however, only internal-memory bisimulation algorithms have been investigated. As the size of real-world DAG data sets often exceeds available main memory, storage in external memory becomes necessary. Hence, there is a practical need for an efficient approach to computing bisimulation in external memory. Our general algorithm has a worst-case IO-complexity of O(Sort(|N| + |E|)), where |N| and |E| are the numbers of nodes and edges, resp., in the data graph and Sort(n) is the number of accesses to external memory needed to sort an input of size n. We also study specializations of this algorithm to common variations of bisimulation for tree-structured XML data sets. We empirically verify efficient performance of the algorithms on graphs and XML documents having billions of nodes and edges, and find that the algorithms can process such graphs efficiently even when very limited internal memory is available. The proposed algorithms are simple enough for practical implementation and use, and open the door for further study of external-memory bisimulation algorithms. To this end, the full open-source C++ implementation has been made freely available

Pattern Mining and Events Discovery in Molecular Dynamics Simulations Data

Molecular dynamics simulation method is widely used to calculate and understand a wide range of properties of materials. A lot of research efforts have been focused on simulation techniques but relatively fewer works are done on methods for analyzing the simulation results. Large-scale simulations usually generate massive amounts of data, which make manual analysis infeasible, particularly when it is necessary to look into the details of the simulation results. In this dissertation, we propose a system that uses computational method to automatically perform analysis of simulation data, which represent atomic position-time series. The system identifies, in an automated fashion, the micro-level events (such as the bond formation/breaking) that are connected to large movements of the atoms, which is considered to be relevant to the diffusion property of the material. The challenge is how to discover such interesting atomic activities which are the key to understanding macro-level (bulk) properties of material. Furthermore, simply mining the structure graph of a material (the graph where the constituent atoms form nodes and the bonds between the atoms form edges) offers little help in this scenario. It is the patterns among the atomic dynamics that may be good candidate for underlying mechanisms. We propose an event-graph model to model the atomic dynamics and propose a graph mining algorithm to discover popular subgraphs in the event graph. We also analyze such patterns in primitive ring mining process and calculate the distributions of primitive rings during large and normal movement of atoms. Because the event graph is a directed acyclic graph, our mining algorithm uses a new graph encoding scheme that is based on topological- sorting. This encoding scheme also ensures that our algorithm enumerates candidate subgraphs without any duplication. Our experiments using simulation data of silica liquid show the effectiveness of the proposed mining system

Traversing large graphs in realistic settings

The notion of graph traversal is of fundamental importance to solving many computational problems. In many modern applications involving graph traversal such as those arising in the domain of social networks, Internet based services, fraud detection in telephone calls etc., the underlying graph is very large and dynamically evolving. This thesis deals with the design and engineering of First Search (BFS) algorithms for massive sparse undirected graphs. Our pipelined implementations with low constant factors, together with some heuristics preserving the worst-case guarantees makes BFS viable on massive graphs. We perform an extensive set of experiments to study the effect of various graph properties such as diameter, inititraversal algorithms for such graphs. We engineer various I/O-efficient Breadth al disk layouts, tuning parameters, disk parallelism, cache-obliviousness etc. on the relative performance of these algorithms. We characterize the performance of NAND flash based storage devices, including many solid state disks. We show that despite the similarities between flash memory and RAM (fast random reads) and between flash disk and hard disk (both are block based devices), the algorithms designed in the RAM model or the external memory model do not realize the full potential of the flash memory devices. We also analyze the effect of misalignments, aging, past I/O patterns, etc. on the performance obtained on these devices. We also consider I/O-efficient BFS algorithms for the case when a hard disk and a solid state disk are used together. We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n2.75)time, independent of the number m of edges inserted. For dense DAGs, this is an improvement over the previous best result of O (min{m3/2 logn,m3/2 +n2 logn}). While our analysis holds only for the incremental setting, our algorithm itself is fully dynamic. We also present the first average-case analysis of online topological ordering algorithms. We prove an expected runtime of O (n2 polylog(n)) under insertion of the edges of a complete DAG in a random order for various incremental topological ordering algorithms.Die Traversierung von Graphen ist von fundamentaler Bedeutung für das Lösen vieler Berechnungsprobleme. Moderne Anwendungen, die auf Graphtraversierung beruhen, findet man unter anderem in sozialen Netzwerken, internetbasierten Dienstleistungen, Betrugserkennung bei Telefonanrufen. In vielen dieser lAnwendungen ist der zugrunde iegende Graph sehr gross und ändert sich kontinuierlich. Wir entwickelnmehrere I/O-effiziente Breitensuch-Algorithmen für massive, dünnbesiedelte, ungerichtete Graphen. Im Zusammenspiel mit Heuristiken zur Einhaltung von Worst-Case-Garantien, ermöglichen unsere pipeline-basierten Implementierungen die Praktikabilität von Breitensuche auf massiven Graphen. Wir führen eine Vielfalt an Experimente durch, um die Wirkung unterschiedlicher Grapheigenschaften zu untersuchen, wie z.B. Graph-Durchmesser, anfängliche Belegung der Festplatte, Tuning-Parameter, Plattenparallelismus. Wir charakterisieren die Leistung von NAND-Flash basierten Speichermedien, einschliesslich vieler solid-state Disks. Wir zeigen, dass trotz der Ähnlichkeiten von Flash-Speicher und RAM (schnelle wahlfreie Lese-Zugriffe) und von Flash-Platten und Festplatten (beide sind blockbasiert) Algorithmen, die für das RAMModell oder das Externspeicher-Modell entworfenen wurden, nicht das volle Potential der Flash-Speicher-Medien ausschöpfen. Zusätzlich analysieren wir die Wirkung von Ausrichtungsfehlern, Alterung, vorausgehenden I/O-Mustern, usw., auf die Leistung dieser Medien. Wir berücksichtigen auch I/O-effiziente Breitensuch-Algorithmen für die gleichzeitige Nutzung von Festplatten und solid-state Disks. Wir stellen einen einfachen Algorithmus vor, der beim Online-Einfügen von Kanten die topologische Ordnung von einem gerichteten, azyklischen Graphen (DAG) mit n Knoten beibehält. Dieser Algorithmus hat eine Laufzeitkomplexität von O(n2.75) unabhängig von der Anzahl m der eingefügten Kanten. Für dichte DAGs ist dies eine Verbesserung des besten, vorherigen Ergebnisses von O(min{m3/2 logn,m3/2 +n2 logn}). Während die Analyse nur im inkrementellen Szenario gütlig ist, ist unser Algorithmus vollständig dynamisch. Ferner stellen wir die erste Average-Case-Analyse von Online-Algorithmen zur Unterhaltung einer topologischen Ordnung vor. Für mehrere inkrementelle Algorithmen, welche die Kanten eines kompletten DAGs in zufälliger Reihenfolge einfügen, beweisen wir eine erwartete Laufzeit von O(n2 polylog(n))

A Practical Parallel Algorithm for Diameter Approximation of Massive Weighted Graphs

We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a weighted graph decomposition strategy generating disjoint clusters of bounded weighted radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee; moreover, for important practical classes of graphs, it runs in a number of rounds asymptotically smaller than those required by the natural approximation provided by the state-of-the-art $\Delta$-stepping SSSP algorithm, which is its only practical linear-space competitor in the aforementioned computational scenario. We complement our theoretical findings with an extensive experimental analysis on large benchmark graphs, which demonstrates that our algorithm attains substantial improvements on a number of key performance indicators with respect to the aforementioned competitor, while featuring a similar approximation ratio (a small constant less than 1.4, as opposed to the polylogarithmic theoretical bound)