The combinatorics of abstract container data types

The study of abstract machines such as Turing machines, push down automata and finite state machines has played an important role in the advancement of computer science. It has led to developments in the theory of general purpose computers, compilers and string manipulation as well as many other areas. The language associated with an abstract machine characterises an important aspect of the behaviour of that machine. It is therefore the principal object of interest when studying such a machine. In this thesis we consider abstract container data types to be abstract machines. We define the concept of a language associated with an abstract container data type and investigate this in the same spirit as for other abstract machines. We also consider a model which allows us to describe various abstract container data types. This model is studied in a similar manner. There is a rich selection of problems to investigate. For instance, the data items which the abstract container data types operate on can take many forms. The input stream could consist of distinct data items, say 1, 2,..., n, or it could be a word over the binary alphabet. Alternatively it could be a sequence formed from the data items in some arbitrary multiset. Another consideration is whether or not an abstract data type has a finite storage capacity. It is shown how to construct a regular grammar which generates (an encoded form of) the set of permutations which can be realised by moving tokens through a network. A one to one correspondence is given between ordered forests of bounded height and members of the language associated with a bounded capacity priority queue operating on binary data. A number of related results are also proved; in particular for networks operating on binary data, and priority queues of capacity 2

Communication-Efficient Probabilistic Algorithms: Selection, Sampling, and Checking

Diese Dissertation behandelt drei grundlegende Klassen von Problemen in Big-Data-Systemen, für die wir kommunikationseffiziente probabilistische Algorithmen entwickeln. Im ersten Teil betrachten wir verschiedene Selektionsprobleme, im zweiten Teil das Ziehen gewichteter Stichproben (Weighted Sampling) und im dritten Teil die probabilistische Korrektheitsprüfung von Basisoperationen in Big-Data-Frameworks (Checking). Diese Arbeit ist durch einen wachsenden Bedarf an Kommunikationseffizienz motiviert, der daher rührt, dass der auf das Netzwerk und seine Nutzung zurückzuführende Anteil sowohl der Anschaffungskosten als auch des Energieverbrauchs von Supercomputern und der Laufzeit verteilter Anwendungen immer weiter wächst. Überraschend wenige kommunikationseffiziente Algorithmen sind für grundlegende Big-Data-Probleme bekannt. In dieser Arbeit schließen wir einige dieser Lücken. Zunächst betrachten wir verschiedene Selektionsprobleme, beginnend mit der verteilten Version des klassischen Selektionsproblems, d. h. dem Auffinden des Elements von Rang $k$ in einer großen verteilten Eingabe. Wir zeigen, wie dieses Problem kommunikationseffizient gelöst werden kann, ohne anzunehmen, dass die Elemente der Eingabe zufällig verteilt seien. Hierzu ersetzen wir die Methode zur Pivotwahl in einem schon lange bekannten Algorithmus und zeigen, dass dies hinreichend ist. Anschließend zeigen wir, dass die Selektion aus lokal sortierten Folgen – multisequence selection – wesentlich schneller lösbar ist, wenn der genaue Rang des Ausgabeelements in einem gewissen Bereich variieren darf. Dies benutzen wir anschließend, um eine verteilte Prioritätswarteschlange mit Bulk-Operationen zu konstruieren. Später werden wir diese verwenden, um gewichtete Stichproben aus Datenströmen zu ziehen (Reservoir Sampling). Schließlich betrachten wir das Problem, die global häufigsten Objekte sowie die, deren zugehörige Werte die größten Summen ergeben, mit einem stichprobenbasierten Ansatz zu identifizieren. Im Kapitel über gewichtete Stichproben werden zunächst neue Konstruktionsalgorithmen für eine klassische Datenstruktur für dieses Problem, sogenannte Alias-Tabellen, vorgestellt. Zu Beginn stellen wir den ersten Linearzeit-Konstruktionsalgorithmus für diese Datenstruktur vor, der mit konstant viel Zusatzspeicher auskommt. Anschließend parallelisieren wir diesen Algorithmus für Shared Memory und erhalten so den ersten parallelen Konstruktionsalgorithmus für Aliastabellen. Hiernach zeigen wir, wie das Problem für verteilte Systeme mit einem zweistufigen Algorithmus angegangen werden kann. Anschließend stellen wir einen ausgabesensitiven Algorithmus für gewichtete Stichproben mit Zurücklegen vor. Ausgabesensitiv bedeutet, dass die Laufzeit des Algorithmus sich auf die Anzahl der eindeutigen Elemente in der Ausgabe bezieht und nicht auf die Größe der Stichprobe. Dieser Algorithmus kann sowohl sequentiell als auch auf Shared-Memory-Maschinen und verteilten Systemen eingesetzt werden und ist der erste derartige Algorithmus in allen drei Kategorien. Wir passen ihn anschließend an das Ziehen gewichteter Stichproben ohne Zurücklegen an, indem wir ihn mit einem Schätzer für die Anzahl der eindeutigen Elemente in einer Stichprobe mit Zurücklegen kombinieren. Poisson-Sampling, eine Verallgemeinerung des Bernoulli-Sampling auf gewichtete Elemente, kann auf ganzzahlige Sortierung zurückgeführt werden, und wir zeigen, wie ein bestehender Ansatz parallelisiert werden kann. Für das Sampling aus Datenströmen passen wir einen sequentiellen Algorithmus an und zeigen, wie er in einem Mini-Batch-Modell unter Verwendung unserer im Selektionskapitel eingeführten Bulk-Prioritätswarteschlange parallelisiert werden kann. Das Kapitel endet mit einer ausführlichen Evaluierung unserer Aliastabellen-Konstruktionsalgorithmen, unseres ausgabesensitiven Algorithmus für gewichtete Stichproben mit Zurücklegen und unseres Algorithmus für gewichtetes Reservoir-Sampling. Um die Korrektheit verteilter Algorithmen probabilistisch zu verifizieren, schlagen wir Checker für grundlegende Operationen von Big-Data-Frameworks vor. Wir zeigen, dass die Überprüfung zahlreicher Operationen auf zwei „Kern“-Checker reduziert werden kann, nämlich die Prüfung von Aggregationen und ob eine Folge eine Permutation einer anderen Folge ist. Während mehrere Ansätze für letzteres Problem seit geraumer Zeit bekannt sind und sich auch einfach parallelisieren lassen, ist unser Summenaggregations-Checker eine neuartige Anwendung der gleichen Datenstruktur, die auch zählenden Bloom-Filtern und dem Count-Min-Sketch zugrunde liegt. Wir haben beide Checker in Thrill, einem Big-Data-Framework, implementiert. Experimente mit absichtlich herbeigeführten Fehlern bestätigen die von unserer theoretischen Analyse vorhergesagte Erkennungsgenauigkeit. Dies gilt selbst dann, wenn wir häufig verwendete schnelle Hash-Funktionen mit in der Theorie suboptimalen Eigenschaften verwenden. Skalierungsexperimente auf einem Supercomputer zeigen, dass unsere Checker nur sehr geringen Laufzeit-Overhead haben, welcher im Bereich von $2\,\%$ liegt und dabei die Korrektheit des Ergebnisses nahezu garantiert wird

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Parallel computation on sparse networks of processors

SIGLELD:D48226/84 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Switching techniques for broadband ISDN

The properties of switching techniques suitable for use in broadband networks have been investigated. Methods for evaluating the performance of such switches have been reviewed. A notation has been introduced to describe a class of binary self-routing networks. Hence a technique has been developed for determining the nature of the equivalence between two networks drawn from this class. The necessary and sufficient condition for two packets not to collide in a binary self-routing network has been obtained. This has been used to prove the non-blocking property of the Batcher-banyan switch. A condition for a three-stage network with channel grouping and link speed-up to be nonblocking has been obtained, of which previous conditions are special cases. A new three-stage switch architecture has been proposed, based upon a novel cell-level algorithm for path allocation in the intermediate stage of the switch. The algorithm is suited to hardware implementation using parallelism to achieve a very short execution time. An array of processors is required to implement the algorithm The processor has been shown to be of simple design. It must be initialised with a count representing the number of cells requesting a given output module. A fast method has been described for performing the request counting using a non-blocking binary self-routing network. Hardware is also required to forward routing tags from the processors to the appropriate data cells, when they have been allocated a path through the intermediate stage. A method of distributing these routing tags by means of a non-blocking copy network has been presented. The performance of the new path allocation algorithm has been determined by simulation. The rate of cell loss can increase substantially in a three-stage switch when the output modules are non-uniformly loaded. It has been shown that the appropriate use of channel grouping in the intermediate stage of the switch can reduce the effect of non-uniform loading on performance

Transient Faults in Computer Systems

A powerful technique particularly appropriate for the detection of errors caused by transient faults in computer systems was developed. The technique can be implemented in either software or hardware; the research conducted thus far primarily considered software implementations. The error detection technique developed has the distinct advantage of having provably complete coverage of all errors caused by transient faults that affect the output produced by the execution of a program. In other words, the technique does not have to be tuned to a particular error model to enhance error coverage. Also, the correctness of the technique can be formally verified. The technique uses time and software redundancy. The foundation for an effective, low-overhead, software-based certification trail approach to real-time error detection resulting from transient fault phenomena was developed

Precise subtyping for asynchronous multiparty sessions

Session subtyping is a cornerstone of refinement of communicating processes: a process implementing a session type (i.e., a communication protocol) T can be safely used whenever a process implementing one of its supertypes T0 is expected, in any context, without introducing deadlocks nor other communication errors. This paper presents the first formalisation of the precise subtyping relation for asynchronous multiparty sessions: we show that the relation is sound (i.e., guarantees safe process replacement, as outlined above) and also complete: any extension of the relation is unsound. Previous work studies precise subtyping for binary sessions (with two participants), or multiparty sessions (with any number of participants) and synchronous interaction. Here, we cover multiparty sessions with asynchronous interaction, where messages are transmitted via FIFO queues (as in the TCP/IP protocol). In this setting, the subtyping relation becomes highly complex: under some conditions, participants can permute the order of their inputs and outputs, by sending some messages earlier, or receiving some later, without causing errors; the precise subtyping relation must capture all such valid permutations, and consequently, its formalisation and proofs become challenging. Our key discovery is a methdology to decompose session types into single input/output session trees, and then express the subtyping relation as a composition of refinement relations between such trees

Techniques for power system simulation using multiple processors

The thesis describes development work which was undertaken to improve the speed of a real-time power system simulator used for the development and testing of control schemes. The solution of large, highly sparse matrices was targeted because this is the most time-consuming part of the current simulator. Major improvements in the speed of the matrix ordering phase of the solution were achieved through the development of a new ordering strategy. This was thoroughly investigated, and is shown to provide important additional improvements compared to standard ordering methods, in reducing path length and minimising potential pipeline stalls. Alterations were made to the remainder of the solution process which provided more flexibility in scheduling calculations. This was used to dramatically ease the run-time generation of efficient code, dedicated to the solution of one matrix structure, and also to reduce memory requirements. A survey of the available microprocessors was performed, which concluded that a special-purpose design could best implement the code generated at run-time, and a design was produced using a microprogrammable floating-point processor, which matched the code produced by the earlier work. A method of splitting the matrix solution onto parallel processors was investigated, and two methods of producing network splits were developed and their results compared. The best results from each method were found to agree well, with a predicted three-fold speed-up for the matrix solution of the C.E.G.B. transmission system from the use of six processors. This gain will increase for the whole simulator. A parallel processing topology of the partitioned network and produce the necessary structures for the remainder of the solution process