Related papers: A characterization of minimum spanning tree-like m…
We study the distributed minimum spanning tree (MST) problem, a fundamental problem in distributed computing. It is well-known that distributed MST can be solved in $\tilde{O}(D+\sqrt{n})$ rounds in the standard CONGEST model (where $n$ is…
We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of…
A vertex of degree one in a tree is called an end vertex and a vertex of degree at least three is called a branch vertex. For a graph $G$, let $\sigma_2$ be the minimum degree sum of two nonadjacent vertices in $G$. We consider tree…
In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…
We consider the problem of designing sublinear time algorithms for estimating the cost of a minimum metric traveling salesman (TSP) tour. Specifically, given access to a $n \times n$ distance matrix $D$ that specifies pairwise distances…
In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…
Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…
Dealing with datasets of very high dimension is a major challenge in machine learning. In this paper, we consider the problem of feature selection in applications where the memory is not large enough to contain all features. In this…
This paper introduces a novel stability measure for edit distances between merge trees of piecewise linear scalar fields. We apply the new measure to various metrics introduced recently in the field of scalar field comparison in scientific…
In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset $V_{\rm NT}$ of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree,…
A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the…
Prediction suffix trees (PST) provide an effective tool for sequence modelling and prediction. Current prediction techniques for PSTs rely on exact matching between the suffix of the current sequence and the previously observed sequence. We…
In this thesis, we study a new disordered system called random spanning tree in random environment (RSTRE) across different families of graphs with varying disorder distributions. We examine several observables as functions of the disorder…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
Given a set of leaf-labeled trees with identical leaf sets, the well-known "Maximum Agreement SubTree" problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its…
The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed…
The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…
A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…
A metric tree ($M$, $d$), also known as $\mathbb{R}$-trees or $T$-theory, is a metric space such that between any two points there is an unique arc and that arc is isometric to an interval in $\mathbb{R}$. In this paper after presenting…
We show that for every $n$-point metric space $M$ there exists a spanning tree $T$ with unweighted diameter $O(\log n)$ and weight $\omega(T) = O(\log n) \cdot \omega(MST(M))$. Moreover, there is a designated point $rt$ such that for every…