Efficient Algorithms and Data Structures for Massive Data Sets

For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are I/O efficient. This thesis adds to the growing chorus of such results. The computational models we use are the external memory model and the W-Stream model. On the external memory model, we obtain the following results. (1) An I/O efficient algorithm for computing minimum spanning trees of graphs that improves on the performance of the best known algorithm. (2) The first external memory version of soft heap, an approximate meldable priority queue. (3) Hard heap, the first meldable external memory priority queue that matches the amortised I/O performance of the known external memory priority queues, while allowing a meld operation at the same amortised cost. (4) I/O efficient exact, approximate and randomised algorithms for the minimum cut problem, which has not been explored before on the external memory model. (5) Some lower and upper bounds on I/Os for interval graphs. On the W-Stream model, we obtain the following results. (1) Algorithms for various tree problems and list ranking that match the performance of the best known algorithms and are easier to implement than them. (2) Pass efficient algorithms for sorting, and the maximal independent set problems, that improve on the best known algorithms. (3) Pass efficient algorithms for the graphs problems of finding vertex-colouring, approximate single source shortest paths, maximal matching, and approximate weighted vertex cover. (4) Lower bounds on passes for list ranking and maximal matching. We propose two variants of the W-Stream model, and design algorithms for the maximal independent set, vertex-colouring, and planar graph single source shortest paths problems on those models.Comment: PhD Thesis (144 pages

Improving the efficiency of parallel minimum spanning tree algorithms

This paper presents results which improve the efficiency of parallel algorithms for computing the minimum spanning trees. For an input graph with n vertices and m edges our EREW PRAM algorithm runs in O(log n) time with O((m+n)√log n) operations. Our CRCW PRAM algorithm runs in O(log n) time with O((m+n)log log n) operations. We also show that for dense graphs we can achieve O(log n) time with O(n2) operations on the EREW PRAM. © 2002 Published by Elsevier Science B.V.link_to_subscribed_fulltex

Efficient Algorithms for a Mesh-Connected Computer with Additional Global Bandwidth

This thesis shows that adding additional global bandwidths to a mesh-connected computer can greatly improve the performance. The goal of this project is to design algorithms for mesh-connected computers augmented with limited global bandwidth, so that we can further enhance our understanding of the parallel/serial nature of the problems on evolving parallel architectures. We do this by first solving several problems associated with fundamental data movement, then summarize ways to resolve different situations one may observe in data movement in parallel computing. This can help us to understand whether the problem is easily parallelizable on different parallel models. We give efficient algorithms to solve several fundamental problems, which include sorting, counting, fast Fourier transform, finding a minimum spanning tree, finding a convex hull, etc. We show that adding a small amount of global bandwidth makes a practical design that combines aspects of mesh and fully connected models to achieve the benefits of each. Most of the algorithms are optimal. For future work, we believe that algorithms with peak-power constrains can make our model well adapted to the recent architectures in high performance computing.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/150001/1/anyujie_1.pd