A parallel Heap-Cell Method for Eikonal equations

Numerous applications of Eikonal equations prompted the development of many efficient numerical algorithms. The Heap-Cell Method (HCM) is a recent serial two-scale technique that has been shown to have advantages over other serial state-of-the-art solvers for a wide range of problems. This paper presents a parallelization of HCM for a shared memory architecture. The numerical experiments in $R^3$ show that the parallel HCM exhibits good algorithmic behavior and scales well, resulting in a very fast and practical solver. We further explore the influence on performance and scaling of data precision, early termination criteria, and the hardware architecture. A shorter version of this manuscript (omitting these more detailed tests) has been submitted to SIAM Journal on Scientific Computing in 2012.Comment: (a minor update to address the reviewers' comments) 31 pages; 15 figures; this is an expanded version of a paper accepted by SIAM Journal on Scientific Computin

{RAMA}: {A} Rapid Multicut Algorithm on {GPU}

We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps executed recursively: (1) Finding conflicted cycles that correspond to violated inequalities of the underlying multicut relaxation, (2) Performing message passing between the edges and cycles to optimize the Lagrange relaxation coming from the found violated cycles producing reduced costs and (3) Contracting edges with high reduced costs through matrix-matrix multiplications. Our algorithm produces primal solutions and dual lower bounds that estimate the distance to optimum. We implement our algorithm on GPUs and show resulting one to two order-of-magnitudes improvements in execution speed without sacrificing solution quality compared to traditional serial algorithms that run on CPUs. We can solve very large scale benchmark problems with up to $\mathcal{O}(10^8)$ variables in a few seconds with small primal-dual gaps. We make our code available at https://github.com/pawelswoboda/RAMA

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms

An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization

Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes