A Sorting Network on Trees

Sorting networks are a class of parallel oblivious sorting algorithms. Not only do they have interesting theoretical properties but they can be fabricated. A sorting network is a sequence of parallel compare-exchange operations using comparators which are grouped into stages. This underlying graph defines the topology of the network. The majority of results on sorting networks concern the unrestricted case where the underlying graph is the complete graph. Prior results are also known for paths, hypercubes, and meshes. In this paper we introduce a sorting network whose underlying topology is a tree and formalize the concept of sorting networks on a restricted graph topology by introducing a new parameter for graphs called its sorting number. The main result of the paper is a description of an [Formula: see text] depth sorting network on a tree with maximum degree [Formula: see text].

SAT and CP - Parallelisation and Applications

In this thesis, we consider the parallelisation and application of SAT and CP solvers. In the first chapter, we consider SAT, the decision problem of propositional logic. We discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Furthermore, we discuss the parallelisation of these solvers with a focus on the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. In the final chapter, we discuss Sorting Networks, which are data oblivious sorting algorithms. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases.

SAT and CP - Parallelisation and Applications

In this thesis, we consider the parallelisation and application of SAT and CP solvers. In the first chapter, we consider SAT, the decision problem of propositional logic. We discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Furthermore, we discuss the parallelisation of these solvers with a focus on the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. In the final chapter, we discuss Sorting Networks, which are data oblivious sorting algorithms. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases.