Related papers: Special Cases of the Minimum Spanning Tree Problem…
In this paper, we consider a coverage problem for uncertain points in a tree. Let T be a tree containing a set P of n (weighted) demand points, and the location of each demand point P_i\in P is uncertain but is known to appear in one of m_i…
We study the problem of exploring all vertices of an undirected weighted graph that is initially unknown to the searcher. An edge of the graph is only revealed when the searcher visits one of its endpoints. Beginning at some start node, the…
Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
We consider cost constrained versions of the minimum spanning tree problem and the assignment problem. We assume edge weights are independent copies of a continuous random variable $Z$ that satisfies $F(x)=\Pr(Z\leq x)\approx x^\alpha$ as…
In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min-max, min-max…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
We study the minimum spanning tree distribution on the space of spanning trees of the $n$-by-$n$ grid for large $n$. We establish bounds on the decay rates of the probability of the most and the least probable spanning trees as…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must be different from those of the MST.…
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…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
We study the minimum spanning arborescence problem on the complete digraph $\vec{K}_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent uniform random variable $U^\alpha$ where $\alpha\leq 1$ and $U$ is…
We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and…
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a…
A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. In this paper we study Minimum Stable Cut, the problem of finding a stable cut of minimum weight. Since this…
We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem,…
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…
Let be given a graph $G=(V,E)$ whose edge set is partitioned into a set $R$ of \emph{red} edges and a set $B$ of \emph{blue} edges, and assume that red edges are weighted and form a spanning tree of $G$. Then, the \emph{Stackelberg Minimum…