RLE Edit Distance in Near Optimal Time

We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mn log(mn)) time. This improves the previous record by a factor of O(n/log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993

Avoiding Ambiguity and Assessing Uniqueness in Minisatellite Alignment

Several algorithms have been suggested for minisatellite alignment. Their time complexity is high -- close to O(n^3) -- due to the necessary reconstruction of duplication histories. We investigate the uniqueness of optimal alignments computed under the common single-copy duplication model. To this extent, it is necessary to avoid ambiguity in the algorithm employed. We re-code the ARLEM algorithm in the form of a grammar, and apply a disambiguation technique which uses a mapping to a canonical representation of minisatellite alignments. Having arrived at a non-ambiguous algorithm this way, we demonstrate that the underlying model -- independent of the algorithm -- gives rise to an exorbitant number of different, co-optimal alignments when applied to real-world data. We conclude that alignment-free methods should be considered for minisatellite comparison

Almost Linear Time Computation of Maximal Repetitions in Run Length Encoded Strings

We consider the problem of computing all maximal repetitions contained in a string that is given in run-length encoding. Given a run-length encoding of a string, we show that the maximum number of maximal repetitions contained in the string is at most m+k-1, where m is the size of the run-length encoding, and k is the number of run-length factors whose exponent is at least 2. We also show an algorithm for computing all maximal repetitions in O(m alpha(m)) time and O(m) space, where alpha denotes the inverse Ackermann function

Compressed bitmap indexes: beyond unions and intersections

Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND,OR,NOT) that are ideally suited for bitmaps. However, it is less obvious how to apply bitmaps to more advanced queries. For example, we might seek products in a store that meet some, but maybe not all, criteria. Such threshold queries generalize intersections and unions; they are often used in information-retrieval and data-mining applications. We introduce new algorithms that are sometimes three orders of magnitude faster than a naive approach. Our work shows that bitmap indexes are more broadly applicable than is commonly believed