The building cost of a spanning tree is the sum of weights of the edges used to construct the spanning tree. The routing cost of a source vertex s on a spanning tree T is the total summation of distances between the source vertex s and all the vertices d in T . Given a source vertices set S, the multiple-source routing cost of a spanning tree T is the summation of the routing costs for source v...

This chapter describes a novel ACO algorithm for the degree-constrained minimum spanning tree (d-MST) problem. Instead of constructing the d-MST directly on the construction graph, ants construct the encoded d-MST. Two well-known tree codings are used: the Prüfer code, and the more recent Blob code (Picciotto, 1999). Both of these tree codings are bijective because they represent each spanning ...

This paper considers k-minimum spanning tree problems. An existing solution algorithm based on tabu search, which was proposed by Katagiri et al., includes an iterative solving procedure of minimum spanning tree (MST) problems for subgraphs to obtain a local optimal solution of k-minimum spanning tree problems. This article provides a new tabu-searchbased approximate solution method that does n...

We study the problem of approximating MST(P ), the Euclidean minimum spanning tree of a set P of n points in [0, 1], by a spanning tree of some subset Q ⊂ P . We show that if the weight of MST(P ) is to be approximated, then in general Q must be large. If the shape of MST(P ) is to be approximated, then this is always possible with a small Q. More specifically, for any 0 < ε < 1 we prove: (i) T...

We study the problem of approximating MST(P ), the minimum weight spanning tree of a set P of n points in [0, 1], by a spanning tree of some subset Q ⊂ P . We show that if the weight of MST(P ) is to be approximated, then in general Q must be large. If the shape of MST(P ) is to be approximated, then this is always possible with a small Q. More specifically, for any 0 < ε < 1 we prove: (i) Ther...

In the rapid increasing usage of wireless sensor networks, fault tolerance is an exigent task to improve the overall performance. In this work we made an attempt using artificial bee colony approach to find data aggregation with fault tolerance in WSN to make an effective use of the existing resources. In this paper it is tried to apply the performance of the Q-MST based fault tolerance mechani...

In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V, E) and a non-negative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized. We obtain an algorithm which returns an MST of maximum degree at most ∆∗+k where ∆∗ is the minimum maximum ...

The performance of the networks is analyzed based on the routing protocols. Usually routing protocols determine the paths based on the network topology and configuration parameters, and not depend on the traffic load on the routers and links. Routing optimization is done using Genetic Algorithm in Minimum Spanning Tree (MST). By using FACE Routing technique, each node is able to gather the loca...