Related papers: The Minimum Spanning Tree of Maximum Entropy
Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay…
A fundamental problem in wireless networks is the \emph{minimum spanning tree} (MST) problem: given a set $V$ of wireless nodes, compute a spanning tree $T$, so that the total cost of $T$ is minimized. In recent years, there has been a lot…
We introduce a new structure for a set of points in the plane and an angle $\alpha$, which is similar in flavor to a bounded-degree MST. We name this structure $\alpha$-MST. Let $P$ be a set of points in the plane and let $0 < \alpha \le…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
This paper describes a generalization of previous methods for constructing tree-structured belief network with hidden variables. The major new feature of the described method is the ability to produce a tree decomposition even when there…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the Minimum Spanning Tree problem, in which the costs associated with every edge of the input graph are vectors. In this paper, we design a new dynamic programming…
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural…
For minimally rigid graphs, the same edge-length data can admit multiple realizations (up to translations and rotations). Finding graphs with exceptionally many realizations is an extremal problem in rigidity theory, but exhaustive search…
We developed a source detection algorithm based on the Minimal Spanning Tree (MST), that is a graph-theoretical method useful for finding clusters in a given set of points. This algorithm is applied to gamma-ray bidimensional images where…
The Steiner Tree Problem (STP) in graphs is an important problem with various applications in many areas such as design of integrated circuits, evolution theory, networking, etc. In this paper, we propose an algorithm to solve the STP. The…
Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very…
A mobile sensor network is a wireless network of sensor nodes that move arbitrarily. In this paper, we explore the use of a maximum stability spanning tree-based data gathering (Max.Stability-DG) algorithm and a minimum-distance spanning…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
The quadratic minimum spanning tree problem (QMSTP) is the problem of finding a spanning tree of a graph such that the total interaction cost between pairs of edges in the tree is minimized. We first show that most of the bounding…
The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the…
Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A…