Related papers: Splay Top Trees
This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural…
Many data sets, crucial for today's applications, consist essentially of enormous networks, containing millions or even billions of elements. Having the possibility of visualizing such networks is of paramount importance. We propose an…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
We address the problem of representing dynamic graphs using $k^2$-trees. The $k^2$-tree data structure is one of the succinct data structures proposed for representing static graphs, and binary relations in general. It relies on compact…
We introduce a notion for hierarchical graph clustering which we call the expander hierarchy and show a fully dynamic algorithm for maintaining such a hierarchy on a graph with $n$ vertices undergoing edge insertions and deletions using…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
Acting on time-critical events by processing ever growing social media or news streams is a major technical challenge. Many of these data sources can be modeled as multi-relational graphs. Continuous queries or techniques to search for rare…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
Recently, graphs have been widely used to represent many different kinds of real world data or observations such as social networks, protein-protein networks, road networks, and so on. In many cases, each node in a graph is associated with…
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 tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
Graph data structures offer a versatile and powerful means to model relationships and interconnections in various domains, promising substantial advantages in data representation, analysis, and visualization. In games, graph-based data…
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…
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…
A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E) encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can be iteratively constructed by n-1 maximum flow computations. They solve the multiterminal…