DAFSA: a Python library for Deterministic Acyclic Finite State Automata [Software]

This work describes dafsa, a Python library for computing graphs from lists of strings for identifying, visualizing, and inspecting patterns of substrings. The library is designed for usage by linguists in studies on morphology and formal grammars, and is intended for faster, easier, and simpler generation of visualizations. It collects frequency weights by default, it can condense structures, and it provides several export options. Figure 1 depicts a basic DAFSA, based upon five English words and generated with default settings

Building Efficient and Compact Data Structures for Simplicial Complexes

The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper, we show how to optimally compress the Simplex Tree while retaining its functionalities. In addition, we propose two new data structures called the Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201

Planar Reachability in Linear Space and Constant Time

We show how to represent a planar digraph in linear space so that distance queries can be answered in constant time. The data structure can be constructed in linear time. This representation of reachability is thus optimal in both time and space, and has optimal construction time. The previous best solution used $O(n\log n)$ space for constant query time [Thorup FOCS'01].Comment: 20 pages, 5 figures, submitted to FoC

Fast Label Extraction in the CDAWG

The compact directed acyclic word graph (CDAWG) of a string $T$ of length $n$ takes space proportional just to the number $e$ of right extensions of the maximal repeats of $T$, and it is thus an appealing index for highly repetitive datasets, like collections of genomes from similar species, in which $e$ grows significantly more slowly than $n$. We reduce from $O(m\log{\log{n}})$ to $O(m)$ the time needed to count the number of occurrences of a pattern of length $m$, using an existing data structure that takes an amount of space proportional to the size of the CDAWG. This implies a reduction from $O(m\log{\log{n}}+\mathtt{occ})$ to $O(m+\mathtt{occ})$ in the time needed to locate all the $\mathtt{occ}$ occurrences of the pattern. We also reduce from $O(k\log{\log{n}})$ to $O(k)$ the time needed to read the $k$ characters of the label of an edge of the suffix tree of $T$, and we reduce from $O(m\log{\log{n}})$ to $O(m)$ the time needed to compute the matching statistics between a query of length $m$ and $T$, using an existing representation of the suffix tree based on the CDAWG. All such improvements derive from extracting the label of a vertex or of an arc of the CDAWG using a straight-line program induced by the reversed CDAWG.Comment: 16 pages, 1 figure. In proceedings of the 24th International Symposium on String Processing and Information Retrieval (SPIRE 2017). arXiv admin note: text overlap with arXiv:1705.0864