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Title: Characteristics and regularities of graphs and words
Author: Christou, Michalis
ISNI:       0000 0004 5368 0230
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2014
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In the last years there has been an increasing interest in discrete structures such as graphs, trees and strings that appear in Mathematics and Computer Science but also in many other interdisciplinary areas including bioinformatics, pattern matching and data compression. We investigate several types of regularities and characteristics appearing in these structures, as well as algorithms for their computation. Graphs are the most popular objects of study in discrete mathematics. We show some progress in external graph theory, i.e. problems which investigate external graphs satisfying certain properties (maximizing planar graphs under girth constrains, degree/diameter problem for trees and pseudo trees, bipartite Ramsey numbers involving stars, stripes and tress). Words, also called strings, are also structures that have acquired great importance in recent years mainly due to their use in DNA modelling. We show some new results regarding the identification and appearance of seeds in strings (a linear time algorithm that computes the minimal left-seed array of a given string, an O(n log n) time algorithm that computes the minimal right-seed arrary given string x, a linear-time solution to compute the maximal left-seed/right-seed array, the appearance of quasiperiodic structures in Fibonacci words and general words). We also show some progress regarding the identification and appearance of abelian regularities in strings (quadratic time algorithms for the identification of all abelian borders of a string, bounds on the number of abelian borders a word and bounds on the lenght of the shortest border of a binary string). Furthermore, we investigate the average number of regularities in a word and we reveal some interesting properties of Padovan words, a family of words related to the Fibonacci sequence. Finally we present a problem on trees: how to output all subtree repeats of a tree in linear time using a string representation of the tree.
Supervisor: Iliopoulos, Costas ; Crochemore, Maxime Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available