相关论文: A combinatorial algorithm to generate all spanning…

In this lecture we will consider the minimum weight spanning tree (MST) problem, i.e., one of the simplest and most vital combinatorial optimization problems. We will discuss a particular greedy algorithm that allows to compute a MST for…

A spanning tree of a network or graph is a subgraph that connects all nodes with the least number or weight of edges. The spanning tree is one of the most straightforward techniques for network simplification and sampling, and for…

Python implementation of selected weighted graph algorithms is presented. The minimal graph interface is defined together with several classes implementing this interface. Graph nodes can be any hashable Python objects. Directed edges are…

An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…

The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…

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…

In a complete graph $K_n$ with edge weights drawn independently from a uniform distribution $U(0,1)$ (or alternatively an exponential distribution $\operatorname{Exp}(1)$), let $T_1$ be the MST (the spanning tree of minimum weight) and let…

We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…

We present an implementation and an experimental evaluation of an algorithm that, given a connected graph G (represented by adjacency lists), estimates in sublinear time, with a relative error, the Minimum Spanning Tree Weight of G; the…

We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…

The weighted spanning tree enumerator of a graph $G$ with weighted edges is the sum of the products of edge weights over all the spanning trees in $G$. In the special case that all of the edge weights equal $1$, the weighted spanning tree…

There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…

This paper investigates the problem of regression model generation. A model is a superposition of primitive functions. The model structure is described by a weighted colored graph. Each graph vertex corresponds to some primitive function.…

The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…

Many dynamic programming algorithms for discrete 0-1 optimizationproblems are "pure" in that their recursion equations only use min/max and addition operations, and do not depend on actual input weights. The well-known greedy algorithm of…

We present a new algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of any (non-negatively) real-weighted graph $G = (V,E,\omega)$. As an intermediate step, we use a new, fast, linear-time…

Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…

In the present paper we consider the problem of constructing all the projective rooted spanning trees of a given graph. We propose an algorithm based on reducing this problem to the problem of constructing all the maximal independent sets…

We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals $T$ require varying priority, level, or quality of service. In this problem, we seek to find a minimum cost tree…