Related papers: Two-Dimensional Block Trees
The next-generation Versatile Video Coding (VVC) standard introduces a new Multi-Type Tree (MTT) block partitioning structure that supports Binary-Tree (BT) and Ternary-Tree (TT) splits in both vertical and horizontal directions. This new…
Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully…
It is commonly accepted in the practice of on-line analytical processing of databases that the multidimensional database organization is less scalable than the relational one. It is easy to see that the size of the multidimensional…
Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…
The {\em wavelet tree} is a flexible data structure that permits representing sequences $S[1,n]$ of symbols over an alphabet of size $\sigma$, within compressed space and supporting a wide range of operations on $S$. When $\sigma$ is…
The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…
Point cloud compression is a key enabler for the emerging applications of immersive visual communication, autonomous driving and smart cities, etc. In this paper, we propose a hybrid point cloud attribute compression scheme built on an…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
The connection of edges in a graph generates a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this work, we present…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
The dynamic trees problem is to maintain a tree under edge updates while supporting queries like connectivity queries or path queries. Despite the first data structure for this fundamental problem -- the link-cut tree -- being invented 40…
For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components. A vertex separator $S$ is minimal if it contains no other separator as a strict subset and a minimum vertex separator is a minimal…
The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 (Bonnet et. al. 2020), a mass of new results has appeared relating twin…
We present a novel lossless universal source coding algorithm that uses parallel computational units to increase the throughput. The length-$N$ input sequence is partitioned into $B$ blocks. Processing each block independently of the other…
The task of accumulating a portion of a list of values, whose values may be updated at any time, is widely used throughout various applications in computer science. While it is trivial to accomplish this task without any constraints,…
Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…
Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success…
Containerization simplifies the sharing and deployment of applications when environments change in the software delivery chain. To deploy an application, container delivery methods push and pull container images. These methods operate on…
Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational…
We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data…