Στόχος της παρούσας διπλωματικής εργασίας είναι να παρουσιάσει τις τεχνικές και τις μεθόδους που πρέπει να ακολουθηθούν για να διαμεριστούν οι κορυφές ενός απλού γραφήματος σε ομάδες κορυφών, οι οποίες κατέχουν όμοιες ή παρόμοιες δομές σύνδεσης με άλλες ομάδες. Η διπλωματική εργασία αποτελείται από τέσσερα μέρη. Στο πρώτο μέρος της εργασίας δίνεται ο ορισμός του απλού γραφήματος, της ομαδοποίησης, του μπλοκ και του μοντέλου των μπλοκ, έννοιες οι οποίες είναι απαραίτητες για την συνέχεια. Στο δεύτερο μέρος περιγράφονται δύο τύποι ισοδυναμίας, που χρησιμοποιούνται για την ομαδοποίηση των κορυφών ενός γραφήματος, καθώς επίσης και δύο μέθοδοι για την επίτευξη της ομαδοποίησης των κορυφών. Στο τρίτο μέρος δίνεται μια πιο γενική ιδέα για την ομαδοποίηση των κορυφών ενός γραφήματος, η οποία βασίζεται σε μια από τις δυο προηγούμενες μεθόδους προσέγγισης της ομαδοποίησης. Στο τέταρτο και τελευταίο μέρος δίδεται μια επέκταση της ομαδοποίησης πάνω σε διμερή δεδομένα και παρουσιάζονται ατα αποτελέσματα, από την εφαρμογή αυτής της επέκτασης σε ένα εμπειρικό παράδειγμα. / -

Disk performance for random access fares significantly worse compared to sequential access. Time required to transfer random blocks to or from disk is dominated by seeking and rotational delay. To improve the throughput and reduce the latency, one can apply techniques to increase the sequentiality of disk accesses, such as block rearrangement and replication. We introduce an approach to improve read performance by replicating blocks into file system free space at the block level. This makes the replication module independent of the file system and therefore easier to implement and verify. A solution that requires no changes to the file system is also easier to adopt. Supporting a new file system is a matter of writing a user-space component that understands its free block data structures. We implemented a prototype as a stacked device driver for Linux and evaluated its performance on a number of workloads.

The set of non-crossing partitions was first studied by Kreweras in 1972 and was known to play an important role in combinatorics, geometric group theory, and free probability. In particular, it has a natural embedding into the symmetric group, and there is an extensive literature on the asymptotic cycle structures of random permutations. This motivates our study on analogous results regarding the asymptotic block structure of random non-crossing partitions. We first investigate an analogous result of the asymptotic distribution for the total number of cycles of random permutations due to Goncharov in 1940's: Goncharov showed that the total number of cycles in a random permutation is asymptotically normally distributed with mean log(n) and variance log(n). As a analog of this result, we show that the total number of blocks in a random non-crossing partition is asymptotically normally distributed with mean n/2 and variance n/8. We also investigate the outer blocks, which arise naturally from non-crossing partitions and has many connections in combinatorics and free probability. It is a surprising result that among many blocks of non-crossing partitions, the expected number of outer blocks is asymptotically 3. We further computed the asymptotic distribution for the total number of blocks, which is a shifted negative binomial distribution.

Disk performance for random access fares significantly worse compared to sequential access. Time required to transfer random blocks to or from disk is dominated by seeking and rotational delay. To improve the throughput and reduce the latency, one can apply techniques to increase the sequentiality of disk accesses, such as block rearrangement and replication. We introduce an approach to improve read performance by replicating blocks into file system free space at the block level. This makes the replication module independent of the file system and therefore easier to implement and verify. A solution that requires no changes to the file system is also easier to adopt. Supporting a new file system is a matter of writing a user-space component that understands its free block data structures. We implemented a prototype as a stacked device driver for Linux and evaluated its performance on a number of workloads.

Thesis (MSc)--University of Stellenbosch, 2007 / Bibliography. Also available via the Internet.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Mar. 5, 2009). PDF text: vi, 126 p. ; 731 K. UMI publication number: AAT 3336690. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph.D.)--Case Western Reserve University, 2009 / Abstract Department of Biomedical Engineering Title from PDF (viewed on 20 April 2009) Available online via the OhioLINK ETD Center

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, December 1997. / Includes bibliographical references. Also available on the Internet.

Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 1998. / Includes bibliographical references.

Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 1998. / Includes bibliographical references.