Pedro J. Martín

CUDA Solutions for the SSSP Problem

We present several algorithms that solve the single-source shortest-path problem using CUDA. We have run them on a database, composed of hundreds of large graphs represented by adjacency lists and adjacency matrices, achieving high speedups regarding a CPU implementation based on Fibonacci heaps. Concerning correctness, we outline why our solutions work, and show that a previous approach [10] is incorrect.

Algorithmic strategies for optimizing the parallel reduction primitive in CUDA

Many general-purpose applications exploit Graphics Processing Units (GPUs) by executing a set of well-known dataparallel primitives. Those primitives are usually invoked from the host many times, so their throughput has a great impact on the performance of the overall system. Thus, the study of novel algorithmic strategies to optimize their implementation on current devices is an interesting topic to the GPU community. In this paper we focus on optimizing the reduction primitive, which merely reduces a data sequence into a single value using a binary associative operator. Although tree-based and sequential-based algorithms have been already implemented on GPUs, a comparison of both algorithm performance had not been carried out yet. Thus, our first contribution is to present an experimental study of state-of-the-art reduction algorithms on CUDA. Next we introduce two algorithmic optimizations that are integrated into the fastest solution (a sequential-based algorithm), improving its throughput even more. Finally, we replicate this methodology to the segmented version of the primitive, which applies when the input is composed of several independent segments. In this case, it is not clear which algorithm exhibits the best performance, since throughput deeply depends on the distribution of segments along the input. According to our results, tree-based algorithms run faster for small segments, while sequential methods are better for medium and large ones.

Ray casting using a roped BVH with CUDA

In this paper, we present a real-time ray caster implemented on GPU using CUDA. It uses a BVH augmented with ropes that is traversed with ray packets to speed up performance. We present two algorithms making use of ray packets, packet-warp and packet-block, which set the packet size to a warp and a block, respectively. We also analyze the influence of the packet size and packet shape by testing several configurations. Finally, we compare the time results we have obtained to previous related papers over a batch of usual scenes.

A tool for teaching interactions between design patterns

We describe the Patterns+UML tool that has been designed to help students of a first year object-oriented programming (OOP) course to apply design patterns to UML class diagrams, to analyze the code generated after their application, and especially to learn how different design patterns interact each other when they share some classes that play a different role in each pattern.

Reasoning with Preorders and Dynamic Sorts Using Free Variable Tableaux

In this paper we present a three valued many sorted logic for dealing with preorders, incorporating subsort relations into the syntax of the language, and where formulas taking the third boolean value as interpretation contain a term or a predicate which is not well-sorted w.r.t. the signature. For this logic a ground tableau-based deduction method and a free variable extension version are proposed, proving their completeness.

A Tool for Automatic Code Generation from Schemas

Algorithm design is one of the more neglected aspects in programming introduction courses. On the contrary, schemas focus on solution construction, since they gather common characteristics of algorithms, so they can be considered as algorithm cognitive units. In this paper, we go beyond the benefits of teaching schemas and we present a tool that incorporates their use. It automatically generates code from the application of schemas, allowing its integration into the class as a useful educational tool.

Tableau Methods for a Logic with Term Declarations

We study free variable tableau methods for logics with term declarations. We show how to define a substitutivity rule preserving the soundness of the tableaux and we prove that some other attempts lead to unsound systems. Based on this rule, we define a sound and complete free variable tableau system and we show how to restrict its application to close branches by defining a sorted unification calculus.

Free Variable Tableaux for a Logic with Term Declarations

We study free variable tableau methods for logics with term declarations. We show how to define a substitutivity rule preserving the soundness of the tableaux and we prove that some other attempts lead to unsound systems. Based on this rule, we define a sound and complete free variable tableau system and we show how to restrict its application to close branches by defining a sorted unification calculus.

Simultaneous Rigid Sorted Unification for Tableaux

In this paper we integrate a sorted unification calculus into free variable tableau methods for logics with term declarations. The calculus we define is used to close a tableau at once, unifying a set of equations derived from pairs of potentially complementary literals occurring in its branches. Apart from making the deduction system sound and complete, the calculus is terminating and so, it can be used as a decision procedure. In this sense we have separated the complexity of sorts from the undecidability of first order logic.

Free-variable tableaux for monotonic preorders

Monotonic preorders are integrated into tableaux using a simultaneous rigid unification calculus. For the case where monotonicity is not considered, a sound, complete and terminating calculus is defined and subsequently refined by using rewrite techniques. For the monotonic case, a sound and existentially complete calculus is presented which avoids the computation of some naive solutions.