Distributed Verification of Minimum Spanning Trees
Authors: Amos Korman, Shay Kutten
Problem Statement: A graph and a tree is given as input in a distributed manner and the algorithm is should be able to verifiy if the tree is a Minimum Spanning Tree (MST).
Detailed Explanation of the Problem Statement
Definitions
Spanning tree: A spanning tree of an undirected graph is a subgraph which is a tree and includes all the vertices of G.
Minimum Spanning Tree (MST) : A spanning tree of a graph whose weight (sum of weight of its edges) is less than or equal to the weight of all other spanning trees of the graph.
Verification of a Spanning Tree: A graph and a tree is given as input and the algorithm should check if the tree is an MST for the graph.
In distributed verification of Minimum Spanning Trees, the input is provided in a distributed manner which means that each node of the graph knows which of its edges belong to the tree. A node does not have any knowledge of the edges which do not emanate from it. The verification algorithm should label the vertices of the graph so that every node, given its own label and the labels of its neighbours only is able to detect if these edges are MST edges or not and whether the input tree is an MST.
Motivation
The motivation for working on verification algorithms is that verification is easier than computation. In a distributed setting verification is even more important because the tree is given in a distributed manner and computing such a
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