While there are distributed algorithms for the Minimum Spanning Tree (MST) problem, these algorithms require relatively large number of messages and time, and are fairly involved, making them impractical for resource-constrained networks such as wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient. Motivat...

Given a graph and a set of vertices, searching for a connected and minimum cost structure which spans the vertices is a classic problem. When no constraints are applied, the minimum cost spanning structure is a sub-graph corresponding to a tree. If all the vertices in the graph should be spanned the problem is referred to as minimum spanning tree (MST) construction and polynomial time algorithm...

We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(m logα(m,n)) time, where α is the inverse-Ackermann function. This improves upon a long standing bound of O(mα(m,n)) established by Tarjan. Our algorithms are based on an efficient split-findmin data structure, which maintains a collection of sequences of weighted eleme...

We consider the problem of locally constructing a spanning subgraph that approximates the Euclidean minimum spanning tree of a unit disk graph. We show that for any k ≥ 2 there exists a klocalized distributed algorithm that, given a unit disk graph U in the plane, constructs a planar subgraph of U containing a Euclidean MST on V (U), whose degree is at most 6, and whose total weight is at most ...

This paper addresses the problem of broadcasting and multicasting in large scale multihop ad hoc wireless networks. We focus on the energy-efficient broadcast routing in stationary networks and consider the case where wireless nodes can dynamically control their transmission power for each broadcast session. Minimum spanning tree (MST) has the property that the longest edge in the tree is the s...

Given a graph G and degree bound B on its nodes, the bounded-degree minimum spanning tree (BDMST) problem is to find a minimum cost spanning tree among the spanning trees with maximum degree B. This bi-criteria optimization problem generalizes several combinatorial problems, including the Traveling Salesman Path Problem (TSPP). An (α, f(B))-approximation algorithm for the BDMST problem produces...

Power conservation is a critical issue for ad hoc wireless networks. The main objective of the paper is to find the minimum uniform transmission power of an ad hoc wireless network, where each node uses the same transmission power, while maintaining network connectivity. Three different algorithms, binary search, Prim’s MST and its extension are developed to solve the problem, and their perform...