On the probabilistic min spanning tree Problem

On the PROBABILISTIC MIN SPANNING TREE

We study a probabilistic optimization model for MIN SPANNING TREE, where any vertex vi of the input-graph G(V, E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Supposing that when this “real” instance G′ becomes known, a decision maker might have no time to perform computation from scratch, we assume that a spanning tree T , called anticipator...

The probabilistic minimum spanning tree problem

In this paper we consider a natural probabilistic variation of the classical minimum spanning tree problem (MST), which we call the probabilistic minimum spanning tree problem (PMST). In particular, we consider the case where not all the points are deterministically present, but are present with certain probability. We discuss the applications of the PMST and find a closed-form expression for t...

8.1 Min Degree Spanning Tree

This problem cab be shown to be NP-Hard by reducing Hamiltonian path to it. Essentially existence of a spanning tree of max degree two is equivalent to a having a Hamiltonian path in the graph. This also shows that the best approximation we can hope for (unless P = NP) is ∆∗ + 1 where ∆∗ is the max degree of the optimal tree. Note that we usually express approximations in a multiplicative form,...

Probabilistic Analysis of the Degree Bounded Minimum Spanning Tree Problem

In the b-degree constrained Euclidean minimum spanning tree problem (bMST) we are given n points in [0; 1] and a degree constraint b 2. The aim is to nd a minimum weight spanning tree in which each vertex has degree at most b. In this paper we analyze the probabilistic version of the problem and prove in a rmative the conjecture of Yukich stated in 1998 on the asymptotics of the problem for uni...

On the Minimum Label Spanning Tree Problem