Related papers: Low-Degree Spanning Trees of Small Weight

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…

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…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph…

The Euclidean Steiner Tree Problem (EST) seeks a minimum-cost tree interconnecting a given set of terminal points in the Euclidean plane, allowing the use of additional intersection points. In this paper, we consider two variants that…

We give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower…

We consider the message complexity of verifying whether a given subgraph of the communication network forms a tree with specific properties both in the KT-$\rho$ (nodes know their $\rho$-hop neighborhood, including node IDs) and the KT-$0$…

The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an $n$-node input graph to be read sequentially in $p$ passes using $\tilde{O}(n)$ space. In this…

Given a directed simple graph G=(V,E) and a nonnegative-valued cost function the power of a vertex u in a directed spanning subgraph H is given by the maximum cost of an arcs of H exiting u. The power of H is the sum of the power of its…

We study the noise sensitivity of the minimum spanning tree (MST) of the $n$-vertex complete graph when edges are assigned independent random weights. It is known that when the graph distance is rescaled by $n^{1/3}$ and vertices are given…

Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a rooted directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover…

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…

Given a graph $G$, a cost function on the non-edges of $G$, and an integer $d$, the problem of finding a cheapest globally rigid supergraph of $G$ in $\mathbb{R}^d$ is NP-hard for $d\geq 1$. For this problem, which is a common…

A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…

A spanning tree $T$ in a graph $G$ is a sub-graph of $G$ with the same vertex set as $G$ which is a tree. In 1981, McKay proved an asymptotic result regarding the number of spanning trees in random $k$-regular graphs. In this paper we prove…

We study search trees with 2-way comparisons (2WCST's), which involve separate less-than and equal-to tests in their nodes, each test having two possible outcomes, yes and no. These trees have a much subtler structure than standard search…

The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…

A fundamental problem for wireless ad hoc networks is the assignment of suitable transmission powers to the wireless devices such that the resulting communication graph is connected. The goal is to minimize the total transmit power in order…

We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio both $\frac{4}{3}$. Using a common theme, the algorithms and their…

Let $R$ and $B$ be two disjoint sets of points in the plane where the points of $R$ are colored red and the points of $B$ are colored blue, and let $n=|R\cup B|$. A bichromatic spanning tree is a spanning tree in the complete bipartite…