Related papers: Maintaining Information in Fully-Dynamic Trees wit…
Evolving trees arise in many real-life scenarios from computer file systems and dynamic call graphs, to fake news propagation and disease spread. Most layout algorithms for static trees do not work well in an evolving setting (e.g., they…
In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently…
We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in dynamic graphs. In an $m$-edge graph undergoing edge insertions and deletions, our data structures give the first…
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…
We present a new data structure for maintaining dynamic permutations, which we call a $\textit{forest of splay trees (FST)}$. The FST allows one to efficiently maintain the cycle structure of a permutation $\pi$ when the allowed updates are…
Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
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…
We present the first dynamic algorithms for Dyck and tree edit distances with subpolynomial update times. Dyck edit distance measures how far a parenthesis string is from a well-parenthesized expression, while tree edit distance quantifies…
SPQR-trees are a central component of graph drawing and are also important in many further areas of computer science. From their inception onwards, they have always had a strong relation to dynamic algorithms maintaining information, e.g.,…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…
Topological structures such as the merge tree provide an abstract and succinct representation of scalar fields. They facilitate effective visualization and interactive exploration of feature-rich data. A merge tree captures the topology of…
Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…
We present a dynamic data structure for representing a graph $G$ with tree-depth at most $D$. Tree-depth is an important graph parameter which arose in the study of sparse graph classes. The structure allows addition and removal of edges…
We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set $S$ of $w$-bit numbers under insertions, deletions, and predecessor queries (return the largest element in $S$ no larger…
Dynamic trees, originally described by Sleator and Tarjan, have been studied deeply for non persistent structures providing $\mathcal{O}(\log n)$ time for update and lookup operations as shown in theory and practice by Werneck. However,…
A tree view or tree navigator is used to display hierarchical data organized in the form of a tree. In a tree structure there are parent and child nodes. The child nodes may further have descendants to n levels. There are many methods to…
We develop a new algorithmic framework for designing approximation algorithms for cut-based optimization problems on capacitated undirected graphs that undergo edge insertions and deletions. Specifically, our framework dynamically maintains…