Related papers: A Solution of Degree Constrained Spanning Tree Usi…
Along with the development of manufacture and services, the problem of distribution network optimization has been growing in importance, thus receiving much attention from the research community. One of the most recently introduced network…
Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired by the process of natural selection among individuals in a population. Despite their widespread use, a comprehensive theoretical analysis of these…
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…
In the k-arc connected subgraph problem, we are given a directed graph G and an integer k and the goal is the find a subgraph of minimum cost such that there are at least k-arc disjoint paths between any pair of vertices. We give a simple…
For an $m$-edge connected simple graph $G$, finding a spanning tree of $G$ with the maximum number of leaves is MAXSNP-complete. The problem remains NP-complete even if $G$ is planar and the maximal degree of $G$ is at most four. Lu and…
In the past decade, significant research has been carried out for realizing intelligent network routing using advertisement, position and near-optimum node selection schemes. In this paper, a grade-based two-level node selection method…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
The inference of minimum spanning arborescences within a set of objects is a general problem which translates into numerous application-specific unsupervised learning tasks. We introduce a unified and generic structure called edit…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
Network design problems aim to compute low-cost structures such as routes, trees and subgraphs. Often, it is natural and desirable to require that these structures have small hop length or hop diameter. Unfortunately, optimization problems…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
Evolutionary computing, particularly genetic algorithm (GA), is a combinatorial optimization method inspired by natural selection and the transmission of genetic information, which is widely used to identify optimal solutions to complex…
Chordal graphs form one of the most studied graph classes. Several graph problems that are NP-hard in general become solvable in polynomial time on chordal graphs, whereas many others remain NP-hard. For a large group of problems among the…
All Colors Shortest Path problem defined on an undirected graph aims at finding a shortest, possibly non-simple, path where every color occurs at least once, assuming that each vertex in the graph is associated with a color known in…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected…
Gravitational-wave detection strategies are based on a signal analysis technique known as matched filtering. Despite the success of matched filtering, due to its computational cost, there has been recent interest in developing deep…
We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of…
Given a directed graph $G=(V,A)$, the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree (i.e., an out-branching) with as many leaves as possible. By designing a Branch-and-Reduced algorithm combined with…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…