1 research outputs found
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