Distributed Maintenance of a Spanning Tree Using Labeled Tree Encoding

Abstract

Maintaining spanning trees in a distributed fashion is central to many networking applications and selfstabilizing algorithms provide an elegant way of doing it in fault-prone environments. In this paper, we propose a self-stabilizing algorithm for maintaining a spanning tree in a distributed fashion for a completely connected topology. Our algorithm requires a node to process O(1) messages on average in one asynchronous round as compared to previous algorithms which need to process messages from every neighbor, resulting in O(n) work in a completely connected topology. Our algorithm also stabilizes faster than the previous approaches. Our approach demonstrates a new methodology which uses the idea of core and non-core states for developing self-stabilizing algorithms. The algorithm is also useful in security related applications due to its unique design.

Parallel Algorithms for Dandelion-Like Codes

“…At the end the path 1 0 is reduced to a single edge (1, 0) and the resulting codeword is g [2], g [3], . .…”

“…For example, they are used in fault dictionary storage [1], distributed spanning tree maintenance [2], generation of random trees [3], Genetic Algorithms [4]. In this paper we restrict our attention to bijective string-based codes in which the length of the string must be equal to n − 2 [5] (n is the number of nodes of the encoded tree).…”

Parallel Algorithms for Encoding and Decoding Blob Code

“…An interesting data structure for representing these trees can be obtained by encoding them by means of strings of node labels. This data structure is useful in many practical applications: Genetic Algorithms [20,28], random uniformly distributed trees generation [10], fault dictionary storage [1], and distributed spanning tree maintenance [14].…”

A Tree-Based Protocol for Enforcing Quotas in Clouds

“…We assume that the physical nodes running the tenant's services are connected using a tree topology that is constructed and maintained using distributed spanning tree algorithms such as that described by Garg et al [17]. Thus, if the local quota on a given node becomes insufficient to meet the tenant's local resource demands, the local quota daemon interacts recursively with its neighboring nodes 1 in the tree to identify those with unused quota allocations.…”

“…It uses a tree-based overlay network to exchange free quota units with other nodes. We assume that the nodes in the system are completely connected, forming a tree-based topology over a real network (e.g., [17]). The global quota is initially distributed randomly over the tree's nodes.…”