4 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
Soft Sequence Heaps
Chazelle [JACM00] introduced the soft heap as a building block for efficient
minimum spanning tree algorithms, and recently Kaplan et al. [SOSA2019] showed
how soft heaps can be applied to achieve simpler algorithms for various
selection problems. A soft heap trades-off accuracy for efficiency, by allowing
of the items in a heap to be corrupted after a total of
insertions, where a corrupted item is an item with artificially increased key
and is a fixed error parameter. Chazelle's soft heaps
are based on binomial trees and support insertions in amortized
time and extract-min operations in amortized time.
In this paper we explore the design space of soft heaps. The main
contribution of this paper is an alternative soft heap implementation based on
merging sorted sequences, with time bounds matching those of Chazelle's soft
heaps. We also discuss a variation of the soft heap by Kaplan et al.
[SICOMP2013], where we avoid performing insertions lazily. It is based on
ternary trees instead of binary trees and matches the time bounds of Kaplan et
al., i.e. amortized insertions and amortized
extract-min. Both our data structures only introduce corruptions after
extract-min operations which return the set of items corrupted by the
operation.Comment: 16 pages, 3 figure
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book