Related papers: Minimal Spanning Tree graphs and power like scalin…
We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform…
In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a…
Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…
Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
Cryptocurrencies such as Bitcoin and Ethereum have recently gained a lot of popularity, not only as a digital form of currency but also as an investment vehicle. Online marketplaces and exchanges allow users across the world to convert…
Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
Previous studies has shown that for a weighted undirected graph having $n$ vertices and $m$ edges, a minimal weight spanning tree can be found with $O^*(\sqrt{mn})$ calls to the weight oracle. The present note shows that a given spanning…
This study uses hierarchical structure methods (minimal spanning tree, (MST) and hierarchical tree, (HT)) to examine the hierarchical structures of the United State (US) foreign trade by using the real prices of their commodity export and…
The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree $T$ in a given graph $G$ with the fewest branch vertices, defined as vertices with a degree three or more in $T$. This problem, known to be NP-hard, has…
In length-constrained minimum spanning tree (MST) we are given an $n$-node graph $G = (V,E)$ with edge weights $w : E \to \mathbb{Z}_{\geq 0}$ and edge lengths $l: E \to \mathbb{Z}_{\geq 0}$ along with a root node $r \in V$ and a…
This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we…
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…
We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained…
We empirically investigated the effects of market factors on the information flow created from N(N-1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is…
This paper uses two hierarchical techniques, a minimal spanning tree and an ultrametric hierarchical tree, to extract a topological influence map for major currencies from the ultrametric distance matrix for 1996-2001. We find that these…
We study the minimum spanning tree (MST) problem in the massively parallel computation (MPC) model. Our focus is particularly on the *strictly sublinear* regime of MPC where the space per machine is $O(n^\delta)$. Here $n$ is the number of…
We present here a topological characterization of the minimal spanning tree that can be obtained by considering the price return correlations of stocks traded in a financial market. We compare the minimal spanning tree obtained from a large…
We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the MST,…