Related papers: Using statistical encoding to achieve tree succinc…
Motivation: Second generation sequencing technology makes it feasible for many researches to obtain enough sequence reads to attempt the de novo assembly of higher eukaryotes (including mammals). De novo assembly not only provides a tool…
In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are…
Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional…
There is a common problem of operating on hash values of elements of some database. In this paper there will be analyzed informational content of such general task and how to practically approach such found lower boundaries. Minimal prefix…
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…
Huffman coding is a widely used method for lossless data compression because it optimally stores data based on how often the characters occur in Huffman trees. An $n$-ary Huffman tree is a connected, cycle-lacking graph where each vertex…
In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once.…
Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…
We combine two methods for the lossless compression of unlabeled graphs - entropy compressing adjacency lists and computing canonical names for vertices - and solve an ensuing novel optimisation problem: Minimum-Entropy Tree-Extraction…
For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…
Sliced Optimal Transport (OT) simplifies the OT problem in high-dimensional spaces by projecting supports of input measures onto one-dimensional lines and then exploiting the closed-form expression of the univariate OT to reduce the…
Barcodes like QR Codes have made that encoded messages have entered our everyday life, what suggests to attach them a second layer of information: directly available to human receiver for informational or marketing purposes. We will discuss…
Assume that an $N$-bit sequence $S$ of $k$ numbers encoded as Elias gamma codes is given as input. We present space-efficient algorithms for sorting, dense ranking and competitive ranking on $S$ in the word RAM model with word size…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
Deterministic finite automata are one of the simplest and most practical models of computation studied in automata theory. Their conceptual extension is the non-deterministic finite automata which also have plenty of applications. In this…
We introduce low-stretch trees to the visualization community with LSQT, our novel technique that uses quasi-trees for both layout and edge bundling. Our method offers strong computational speed and complexity guarantees by leveraging the…
Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in…
For many kinds of prefix-free codes there are efficient and compact alternatives to the traditional tree-based representation. Since these put the codes into canonical form, however, they can only be used when we can choose the order in…