Abstract

We consider the dominating point set reporting problem in two-dimension. We propose a data structure for finding the set of dominating points inside a given orthogonal query rectangle. Given a set of n points in the plane, it supports 4-sided queries in O (log n+ k), where k is size of the output, using O (n log n) space. This work can be of application when range queries are generated using mobile devices with limited display capacity.

Abstract

In this work we study the problem of finding axesparallel regions of maximum density for weighted point sets in IR2 and IR3. The 2-d variant is motivated by applications in thermal analysis of VLSI chips.

Abstract

Multiplying a sparse matrix with a vector (spmv for short) is a fundamental operation in many linear algebra kernels. Having an efficient spmv kernel on modern architectures such as the GPUs is therefore of principal interest. The computational challenges that spmv poses are significantlydifferent compared to that of the dense linear algebra kernels. Recent work in this direction has focused on designing data structures to represent sparse matrices so as to improve theefficiency of spmv kernels. However, as the nature of sparseness differs across sparse matrices, there is no clear answer as to which data structure to use given a sparse matrix. In this work, we address this problem by devising techniques to understand the nature of the sparse matrix and then choose appropriate data structures accordingly. By using our technique, we are able to improve the performance of the spmv kernel on an Nvidia Tesla GPU (C1060) by a factor of up to80% in some instances, and about 25% on average compared to the best results of Bell and Garland [3] on the standard dataset (cf. Williams et al. SC'07) used in recent literature. We also use our spmv in the conjugate gradient method and show an average 20% improvement compared to using HYB spmv of [3], on the dataset obtained from the The University of Florida Sparse Matrix Collection [9].

Abstract

The advent of multicore and many-core architectures saw them being deployed to speed-up computations across several disciplines and application areas. Prominent examples include semi-numerical algorithms such as sorting, graph algorithms, image processing, scientific computations, and the like. In particular, using GPUs for general purpose computations has attracted a lot of attention given that GPUs can deliver more than one TFLOP of computing power at very low prices. In this work, we use a new model of multicore computing called hybrid multicore computing where the computation is performed simultaneously a control device, such as a CPU, and an accelerator such as a GPU. To this end, we use two case studies to explore the algorithmic and analytical issues in hybrid multicore computing. Our case studies involve two different ways of designing hybrid multicore algorithms. The main contribution of this paper is to address the issues related to the design of hybrid solutions. We show our hybrid algorithm for list ranking is faster by 50% compared to the best known implementation [Z. Wei, J. JaJa; IPDPS 2010]. Similarly, our hybrid algorithm for graph connected components is faster by 25% compared to the best known GPU implementation [26].

Abstract

Graphics processing units provide a large compu-tational power at a very low price which position them as anubiquitous accelerator. General purpose programming on thegraphics processing units (GPGPU) is best suited for regulardata parallel algorithms. They are not directly amenable foralgorithms which have irregular data access patterns suchas list ranking, and finding the connected components of agraph, and the like. In this work, we present a GPU-optimizedimplementation for finding the connected components of agiven graph. Our implementation tries to minimize the impactof irregularity, both at the data level and functional level.Our implementation achieves a speed up of 9 to 12 timesover the best sequential CPU implementation. For instance, ourimplementation finds connected components of a graph of 10million nodes and 60 million edges in about 500 millisecondson a GPU, given a random edge list. We also draw interestingobservations on why PRAM algorithms, such as the Shiloach-Vishkin algorithm may not be a good fit for the GPU and howthey should be modified.

Abstract

Genetic algorithms are effective in solving many optimiza-tion tasks. However, the long execution time associated withit prevents its use in many domains. In this paper, we pro-pose a new approach for parallel implementation of geneticalgorithm on graphics processing units (GPUs) using CUDAprogramming model. We exploit the parallelism within achromosome in addition to the parallelism across multiplechromosomes. The use of one thread per chromosome byprevious efforts does not utilize the GPU resources effec-tively. Our approach uses multiple threads per chromosome,thereby exploiting the massively multithreaded GPU moreeffectively. This results in good utilization of GPU resourceseven at small population sizes while maintaining impressivespeed up for large population sizes. Our approach is mod-eled after the GAlib library and is adaptable to a varietyof problems. We obtain a speedup of over 1500 over theCPU on problems involving a million chromosomes. Prob-lems of such magnitude are not ordinarily attempted due tothe prohibitive computation times.

Abstract

Distance bounding protocols are used by nodes in wireless networks to calculate upper bounds on their distances to other nodes. However, dishonest nodes in the network can turn the calculations both illegitimate and inaccurate when they participate in protocol executions. It is important to analyze protocols for the possibility of such violations. Past efforts to analyze distance bounding protocols have only been manual. However, automated approaches are important since they are quite likely to find flaws that manual approaches cannot, as witnessed in literature for analysis pertaining to key establishment protocols. In this paper, we use the constraint solver tool to automatically analyze distance bounding protocols. We first formulate a new trace property called Secure Distance Bounding (SDB) that protocol executions must satisfy. We then classify the scenarios in which these protocols can operate considering the (dis) honesty of nodes and location of the attacker in the network. Finally, we extend the constraint solver so that it can be used to test protocols for violations of SDB in these scenarios and illustrate our technique on some published protocols.

Abstract

Graphics processing units provide a large compu-tational power at a very low price which position them as an ubiquitous accelerator. General purpose programming on the graphics processing units (GPGPU) is best suited for regular data parallel algorithms. They are not directly amenable for algorithms which have irregular data access patterns such as list ranking, and finding the connected components of a graph, and the like. In this work, we present a GPU-optimized implementation for finding the connected components of a given graph. Our implementation tries to minimize the impact of irregularity, both at the data level and functional level. Our implementation achieves a speed up of 9 to 12 times over the best sequential CPU implementation. For instance, our implementation finds connected components of a graph of 10 million nodes and 60 million edges in about 500 milliseconds on a GPU, given a random edge list. We also draw interesting observations on why PRAM algorithms, such as the Shiloach-Vishkin algorithm may not be a good fit for the GPU and how they should be modified.

Abstract

One important challenge in wireless ad hoc networks is to achieve collision free communication. Many MAC layer protocols have been proposed by considering various communication models of the ad hoc networks. One such protocol is TDMA, which provides for interference free communication while providing some bound on the packet delay. However, most proposed TDMA schemes can perform scheduling transmissions among nodes that are within transmission range. This is due to the simplistic modeling of the underlying network. Recently, more practical network models and overlay construction algorithms have been proposed that consider the interference among nodes as well. Existing TDMA protocols are unsuitable for such models as they will have to consider the interference range of the nodes as well. This requires that the TDMA protocol operate in a global perspective while working as a local-control algorithm. In this work, we describe a novel TDMA protocol that is suitable for such realistic and practical network models. We also extend the TDMA protocol to handle other difficulties such as membership changes within transmission range and interference range. Some networks also have to deal with sleeping nodes that wake up periodically. Our TDMA scheme employs a simple control phase and a data phase to handle such tasks. Some of the benefits of our solution are that no knowledge of the network parameters such as the size or an estimate of the size are used. The overhead of our scheme is also very low and (control) messages exchanged are of small size. Our solution will also be self-stabilizing which is an important property for distributed systems. To the best of our knowledge, our TDMA protocol is the first MAC layer protocol for such realistic network models. Additionally, we report some experimental results of our scheme.

Abstract

Symmetry breaking is a fundamental operation in distributed computing. It has applications to important problems such as graph vertex and edge coloring, maximal independent sets, and the like. Deterministic algorithms for symmetry breaking that run in a polylogarithmic number of rounds are not known. However, randomized algorithms that run in poly-logarithmic number of rounds are known starting from Luby's algorithm. Recently, orientation on edges was considered and it was shown that an O(Δ) coloring of the vertices of a given oriented graph can be arrived at using essentially O(log Δ + √log n) bits of communication. In this paper we further demonstrate the power of orientation on edges in symmetry-breaking. We present efficient algorithms to construct fractional independent sets in constant degree graphs using very low order communication between the vertices. For instance, we show that in bounded degree graphs and planar graphs, it is possible to construct a fractional independent set by exchanging O(1) bits. Further, we present algorithms to construct maximal independent sets in bounded degree graphs and oriented trees. Our algorithm for constructing an MIS of an oriented tree uses only O(log n) bits of communication.