Related papers: Minimum Spanning trees with Neighborhoods
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of…
Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…
Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…
Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to…
We study network loss tomography based on observing average loss rates over a set of paths forming a tree -- a severely underdetermined linear problem for the unknown link loss probabilities. We examine in detail the role of sparsity as a…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…
The cable-trench problem is defined as a linear combination of the shortest path and the minimum spanning tree problem. In particular, the goal is to find a spanning tree that simultaneously minimizes its total length and the total path…
This paper proposes an efficient hypergraph partitioning framework based on a novel multi-objective non-convex constrained relaxation model. A modified accelerated proximal gradient algorithm is employed to generate diverse $k$-dimensional…
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…
Now a days many algorithms are invented or being inventing to find the solution for Euclidean Minimum Spanning Tree, EMST, problem, as its applicability is increasing in much wide range of fields containing spatial or spatio temporal data…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
We present a new branch-and-bound type search method for mixed integer linear optimization problems based on the concept of offshoots (introduced in this paper). While similar to a classic branch-and-bound method, it allows for changing the…