A fully distributed (minimal) spanning tree algorithm

The minimum spanning tree is a classical problem in distributed system environment. We extend this challenge in Cognitive Radio Networks (CRN). In CRN, the spectrum mobility and the node mobility creates connectivity problem during neighbour discovery. Thus, finding edges (or relation graph) between the SU nodes in order to create communication graph for Minimum Spanning Tree (MST) is a challenge in cognitive radio network. In the present work, we propose a solution to the problem of creating minimum spanning tree (MST) in cognitive radio network. It is a message passing based distributed algorithm. The MST algorithm find shortest path between any pairs of SUs (or vertices) in the communication graph of CRN. The communication message complexity of our algorithm is 6E, where E represents the edges. The MST is useful for data dissemination in cognitive radio network.

The minimum spanning tree is useful for data disseminating or broadcasting where a leader node can regulate the data with minimum cost and time. The article presents an algorithm to construct minimum spanning tree in cognitive radio networks. The cognitive radio network works differently with single channel or multi-channel wireless networks than conventional wireless networks. The cognitive radio (or secondary user) nodes have multi-channel accessing capabilities during run time by adjusting the radio parameters according to the available spectrum. The primary user or licensed user holds the spectrum and if it is free, the secondary user can use this for any purpose. Initially, we identify the challenges related to formation of logical structure in cognitive radio network. Then, we present our time and message constrained based cost (or weight) estimation distributed algorithm to construct minimum spanning tree. We describe our algorithm with the help of state diagram representation. The correctness proof of the algorithm is also included.

Sense of direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this property are still not known; in fact, the ongoing investigations continue to bring new (often surprising) results, to establish unsuspected links with other research and/or application areas, and to pose more questions than they answer. The aim of this paper is to provide a view of the current status of research, describing some of the relevant results, and providing pointers to future research directions.

Spanning trees help removing cycles and establishing short paths between a given node and the rest of the nodes in a network. In ad hoc mobile computing networks, however, transient node failures occur due to being out of range or powered off. Therefore, we present a self-stabilized distributed algorithm based on homogeneous agents for constructing a random spanning tree. Our approach makes use of distributed random walks as a network traversal scheme, in order to handle dynamic topology changes in ad hoc wireless networks. Each random walk is represented by a mobile agent annexing a territory over the underlying network. These multiple random walks collapse into a final one that defines the random spanning tree. It will be shown that, compared to deterministically predetermined spanning trees, our algorithm is more resilient to transient failures that occur in ad hoc mobile networks.

The recursive shortest spanning tree (RSST) algorithm has been used for various image and video coding systems. The speed is very demanding for such applications. However, the RSST algorithm is too complex to perform in a reasonable time. This motivates the present work. A distributed algorithm that constructs a recursive shortest spanning tree for image segmentation with a fixed number of processors is presented in this paper. Using a tailored data partition strategy to assign jobs to processors in our proposed parallel recursive shortest spanning tree (PRSST) algorithm, we derive a new lower bound ofO(n) for one processor with ann-pixel image. The complexity of the proposed algorithm is cost-optimal and the total number of messages required isO(c) for images of any size, wherecis a small constant. The objective quality of segmented images produced by our PRSST has maximum 1.5 dB difference from those generated by Morris's RSST algorithm for images of the size of 128 by 128 and 150 by 150 pixels.

In this paper, we prove a general result on the impact of sense of direction. We show that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast, Depth First Traversal, Election, and Spanning Tree Construction. In systems with n nodes and e communication links, the solution for the Depth First Traversal and the Broadcast problems require $\text{Ω(e)}$ messages with arbitrary labelings; we show that, with any sense of direction, they can be solved exchanging only Θ(n) messages, even if the system is anonymous. The problems of Election and of Spanning Tree Construction require $\text{Ω(e + n log n)}$ messages with arbitrary labelings; on the other hand, we show that they can be solved with Θ(n) messages with any sense of direction. The results presented here completely explain and generalize the existing results which now follow as corollaries for specific labelings.