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

Optimal Codes Detecting Deletions in Concatenated Binary Strings Applied to Trace Reconstruction

Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings. Since deletions alter the lengths of the strings, a fundamental question to ask is: how much redundancy do we need to introduce in $\mathbf{x}$ in order to recover the boundaries of $\mathbf{x}^1,\mathbf{x}^2,\ldots$? This boundary problem is equivalent to the problem of designing codes that can detect the exact number of deletions in each concatenated string. In this work, we answer the question above by first deriving converse results that give lower bounds on the redundancy of deletion-detecting codes. Then, we present a marker-based code construction whose redundancy is asymptotically optimal in $\delta$ among all families of deletion-detecting codes, and exactly optimal among all block-by-block decodable codes. To exemplify the usefulness of such deletion-detecting codes, we apply our code to trace reconstruction and design an efficient coded reconstruction scheme that requires a constant number of traces.Comment: Accepted for publication in the IEEE Transactions on Information Theory. arXiv admin note: substantial text overlap with arXiv:2207.05126, arXiv:2105.0021

The Role of String Similarity Metrics in Ontology Alignment

Tim Berners-Lee originally envisioned a much different world wide web than the one we have today - one that computers as well as humans could search for the information they need [3]. There are currently a wide variety of research efforts towards achieving this goal, one of which is ontology alignment