|M.Sc Student||Trehan Chhaya|
|Subject||Verification and Self Stabilization of DFS|
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Shay Kutten|
|Full Thesis text|
We present algorithms for distributed verification and silent-stabilization of a DFS (Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of O(n log Δ) bits per node and O(nD) respectively, where Δ is the highest degree of a node, n is the number of nodes and
D is the diameter of the network. In contrast, our algorithm has a space complexity of O(log n) bits per node, which is optimal for silent-stabilizing spanning trees and runs in O(n) time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a standalone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, we also present a (non-silent) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones.