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The genome sequence alignment problems are very important ones from the computational biology perspective. These problems deal with large amount of data which is memory intensive as well as computation intensive. In the literature, two separate algorithms have been studied and improved – one is a Pairwise sequence alignment algorithm which aligns pairs of genome sequences with memory reduction and parallelism for the computation and the other one is the multiple sequence alignment algorithm that aligns multiple genome sequences and this algorithm is also parallelized efficiently so that the workload of the alignment program is well distributed. The parallel applications can be launched on different environments where shared memory is very well suited for these kinds of applications. But shared memory environment has the limitation of memory usage as well as scalability also these machines are very costly. A better approach is to use the cluster of computers and the cluster environment can be further enhanced to a grid environment so that the scalability can be improved introducing multiple clusters. Here the grid environment is studied as well as the shared memory and cluster environment for the two applications. It can be stated that for carefully designed algorithms the grid environment is comparable for its performance to other distributed environments and it sometimes outperforms the others in terms of the limitations of resources the other distributed environments have.

Threat modeling for information technology infrastructure can be done using shortest path algorithms in stochastic graphs. By modeling the infrastructure as a graph, potential vulnerabilities may be presented by computing what paths an attacker might take. This thesis project presents and compares two memory efficient algorithms that can be used to solve this problem approximately, the online k-means and sampled k-shortest path algorithm. By computing paths for several different graph types, the two algorithms were compared against a naive algorithm. The online k-means algorithm uses approximately 77 times less memory, executes in the same amount of time, and produces similar path lengths. In our experiments, the sampled k-shortest path algorithm uses approximately 154 times less memory, execution time is seen to be lowered by a factor of 5 to 20 depending on the graph type, but path distances computed are longer.

Consider a time-dependent optimal control problem, where the state evolution is described by an initial value problem. There are a variety of numerical methods to solve these problems. The so-called indirect approach is considered detailed in this thesis. The indirect methods solve decoupled boundary value problems resulting from the necessary conditions for the optimal control problem. The so-called Pantoja method describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. There are many relationships between multiple shooting techniques and Pantoja method, which are investigated in this thesis. In this context, the equivalence of Pantoja method and multiple shooting method of Riccati type is shown. Moreover, Pantoja method is extended to the case where the state equations are discretised using one of implicit numerical methods. Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control problems in ordinary differential equations by Pantoja or Riccati equivalent methods leads to a succession of triple sweeps through the discretised time interval. The second (adjoint) sweep relies on information from the first (original) sweep, and the third (final) sweep depends on both of them. Typically, the steps on the adjoint sweep involve more operations and require more storage than the other two. The key difficulty is given by the enormous amount of memory required for the implementation of these methods if all states throughout forward and adjoint sweeps are stored. One of goals of this thesis is to present checkpointing techniques for memory reduced implementation of these methods. For this purpose, the well known aspect of checkpointing has to be extended to a `nested checkpointing` for multiple transversals. The proposed nested reversal schedules drastically reduce the required spatial complexity. The schedules are designed to minimise the overall execution time given a certain total amount of storage for the checkpoints. The proposed scheduling schemes are applied to the memory reduced implementation of the optimal control problem of laser surface hardening and other optimal control problems. / Es wird ein Problem der optimalen Steuerung betrachtet. Die dazugehoerigen Zustandsgleichungen sind mit einer Anfangswertaufgabe definiert. Es existieren zahlreiche numerische Methoden, um Probleme der optimalen Steuerung zu loesen. Der so genannte indirekte Ansatz wird in diesen Thesen detailliert betrachtet. Die indirekten Methoden loesen das aus den Notwendigkeitsbedingungen resultierende Randwertproblem. Das so genannte Pantoja Verfahren beschreibt eine zeiteffiziente schrittweise Berechnung der Newton Richtung fuer diskrete Probleme der optimalen Steuerung. Es gibt mehrere Beziehungen zwischen den unterschiedlichen Mehrzielmethoden und dem Pantoja Verfahren, die in diesen Thesen detailliert zu untersuchen sind. In diesem Zusammenhang wird die aequivalence zwischen dem Pantoja Verfahren und der Mehrzielmethode vom Riccati Typ gezeigt. Ausserdem wird das herkoemlige Pantoja Verfahren dahingehend erweitert, dass die Zustandsgleichungen mit Hilfe einer impliziten numerischen Methode diskretisiert sind. Weiterhin wird das Symplektische Konzept eingefuehrt. In diesem Zusammenhang wird eine geeignete numerische Methode praesentiert, die fuer ein unrestringiertes Problem der optimalen Steuerung angewendet werden kann. In diesen Thesen wird bewiesen, dass diese Methode symplectisch ist. Das iterative Loesen eines Problems der optimalen Steuerung in gewoenlichen Differentialgleichungen mit Hilfe von Pantoja oder Riccati aequivalenten Verfahren fuehrt auf eine Aufeinanderfolge der Durchlaeufetripeln in einem diskretisierten Zeitintervall. Der zweite (adjungierte) Lauf haengt von der Information des ersten (primalen) Laufes, und der dritte (finale) Lauf haeng von den beiden vorherigen ab. Ueblicherweise beinhalten Schritte und Zustaende des adjungierten Laufes wesentlich mehr Operationen und benoetigen auch wesentlich mehr Speicherplatzkapazitaet als Schritte und Zustaende der anderen zwei Durchlaeufe. Das Grundproblem besteht in einer enormen Speicherplatzkapazitaet, die fuer die Implementierung dieser Methoden benutzt wird, falls alle Zustaende des primalen und des adjungierten Durchlaufes zu speichern sind. Ein Ziel dieser Thesen besteht darin, Checkpointing Strategien zu praesentieren, um diese Methoden speichereffizient zu implementieren. Diese geschachtelten Umkehrschemata sind so konstruiert, dass fuer einen gegebenen Speicherplatz die gesamte Laufzeit zur Abarbeitung des Umkehrschemas minimiert wird. Die aufgestellten Umkehrschemata wurden fuer eine speichereffiziente Implementierung von Problemen der optimalen Steuerung angewendet. Insbesondere betrifft dies das Problem einer Oberflaechenabhaertung mit Laserbehandlung.

Consider a time-dependent optimal control problem, where the state evolution is described by an initial value problem. There are a variety of numerical methods to solve these problems. The so-called indirect approach is considered detailed in this thesis. The indirect methods solve decoupled boundary value problems resulting from the necessary conditions for the optimal control problem. The so-called Pantoja method describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. There are many relationships between multiple shooting techniques and Pantoja method, which are investigated in this thesis. In this context, the equivalence of Pantoja method and multiple shooting method of Riccati type is shown. Moreover, Pantoja method is extended to the case where the state equations are discretised using one of implicit numerical methods. Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control problems in ordinary differential equations by Pantoja or Riccati equivalent methods leads to a succession of triple sweeps through the discretised time interval. The second (adjoint) sweep relies on information from the first (original) sweep, and the third (final) sweep depends on both of them. Typically, the steps on the adjoint sweep involve more operations and require more storage than the other two. The key difficulty is given by the enormous amount of memory required for the implementation of these methods if all states throughout forward and adjoint sweeps are stored. One of goals of this thesis is to present checkpointing techniques for memory reduced implementation of these methods. For this purpose, the well known aspect of checkpointing has to be extended to a `nested checkpointing` for multiple transversals. The proposed nested reversal schedules drastically reduce the required spatial complexity. The schedules are designed to minimise the overall execution time given a certain total amount of storage for the checkpoints. The proposed scheduling schemes are applied to the memory reduced implementation of the optimal control problem of laser surface hardening and other optimal control problems. / Es wird ein Problem der optimalen Steuerung betrachtet. Die dazugehoerigen Zustandsgleichungen sind mit einer Anfangswertaufgabe definiert. Es existieren zahlreiche numerische Methoden, um Probleme der optimalen Steuerung zu loesen. Der so genannte indirekte Ansatz wird in diesen Thesen detailliert betrachtet. Die indirekten Methoden loesen das aus den Notwendigkeitsbedingungen resultierende Randwertproblem. Das so genannte Pantoja Verfahren beschreibt eine zeiteffiziente schrittweise Berechnung der Newton Richtung fuer diskrete Probleme der optimalen Steuerung. Es gibt mehrere Beziehungen zwischen den unterschiedlichen Mehrzielmethoden und dem Pantoja Verfahren, die in diesen Thesen detailliert zu untersuchen sind. In diesem Zusammenhang wird die aequivalence zwischen dem Pantoja Verfahren und der Mehrzielmethode vom Riccati Typ gezeigt. Ausserdem wird das herkoemlige Pantoja Verfahren dahingehend erweitert, dass die Zustandsgleichungen mit Hilfe einer impliziten numerischen Methode diskretisiert sind. Weiterhin wird das Symplektische Konzept eingefuehrt. In diesem Zusammenhang wird eine geeignete numerische Methode praesentiert, die fuer ein unrestringiertes Problem der optimalen Steuerung angewendet werden kann. In diesen Thesen wird bewiesen, dass diese Methode symplectisch ist. Das iterative Loesen eines Problems der optimalen Steuerung in gewoenlichen Differentialgleichungen mit Hilfe von Pantoja oder Riccati aequivalenten Verfahren fuehrt auf eine Aufeinanderfolge der Durchlaeufetripeln in einem diskretisierten Zeitintervall. Der zweite (adjungierte) Lauf haengt von der Information des ersten (primalen) Laufes, und der dritte (finale) Lauf haeng von den beiden vorherigen ab. Ueblicherweise beinhalten Schritte und Zustaende des adjungierten Laufes wesentlich mehr Operationen und benoetigen auch wesentlich mehr Speicherplatzkapazitaet als Schritte und Zustaende der anderen zwei Durchlaeufe. Das Grundproblem besteht in einer enormen Speicherplatzkapazitaet, die fuer die Implementierung dieser Methoden benutzt wird, falls alle Zustaende des primalen und des adjungierten Durchlaufes zu speichern sind. Ein Ziel dieser Thesen besteht darin, Checkpointing Strategien zu praesentieren, um diese Methoden speichereffizient zu implementieren. Diese geschachtelten Umkehrschemata sind so konstruiert, dass fuer einen gegebenen Speicherplatz die gesamte Laufzeit zur Abarbeitung des Umkehrschemas minimiert wird. Die aufgestellten Umkehrschemata wurden fuer eine speichereffiziente Implementierung von Problemen der optimalen Steuerung angewendet. Insbesondere betrifft dies das Problem einer Oberflaechenabhaertung mit Laserbehandlung.

The rampant growth of the Internet has been coupled with an equivalent growth in cyber crime over the Internet. With our increased reliance on the Internet for commerce, social networking, information acquisition, and information exchange, intruders have found financial, political, and military motives for their actions. Network Intrusion Detection Systems (NIDSs) intercept the traffic at an organization’s periphery and try to detect intrusion attempts. Signature-based NIDSs compare the packet to a signature database consisting of known attacks and malicious packet fingerprints. The signatures use regular expressions to model these intrusion activities. This thesis presents a memory efficient pattern matching system for the class of regular expressions appearing frequently in the NIDS signatures. Proposed Cascaded Automata Architecture is based on two stage automata. The first stage recognizes the sub-strings and character classes present in the regular expression. The second stage consumes symbol generated by the first stage upon receiving input traffic symbols. The basic idea is to utilize the research done on string matching problem for regular expression pattern matching. We formally model the class of regular expressions mostly found in NIDS signatures. The challenges involved in using string matching algorithms for regular expression matching has been presented. We introduce length-bound transitions, counter-based states, and associated counter arrays in the second stage automata to address these challenges. The system uses length information along with counter arrays to keep track of overlapped sub-strings and character class based transition. We present efficient implementation techniques for counter arrays. The evaluation of the architecture on practical expressions from Snort rule set showed compression in number of states between 50% to 85%. Because of its smaller memory footprint, our solution is suitable for both software based implementations on network chips as well as FPGA based designs.