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Recall that we discussed the "leader-based" deterministic distributed algorithm for 2-colouring a path, that runs in time O(n) on an n node path network. Suppose we now relax the constraint of 2-colouring to mean, it is okay for one of the neighbours of a node to x get the same colour as the mode x, as long as the other neighbour gets a different colour. The end points must get a different colour from their respective unique neighbours. The running time for a best efficiency deterministic distributed algorithm, using unique identifiers for nodes, for this problem would be:

Recall that we discussed the "leader-based" deterministic distributed algorithm for 2-colouring a path, that runs in time O(n) on an n node path network. Suppose we now relax the constraint of 2-colouring to mean, it is okay for one of the neighbours of a node to x get the same colour as the mode x, as long as the other neighbour gets a different colour. The end points must get a different colour from their respective unique neighbours. The running time for a best efficiency deterministic distributed algorithm, using unique identifiers for nodes, for this problem would be:

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Recall that we discussed the "leader-based" deterministic distributed algorithm for 2-colouring a path, that runs in time O(n) on an n node path network. Suppose we now relax the constraint of 2-colouring to mean, it is okay for one of the neighbours of a node to x get the same colour as the mode x, as long as the other neighbour gets a different colour. The end points must get a different colour from their respective unique neighbours. The running time for a best efficiency deterministic distributed algorithm, using unique identifiers for nodes, for this problem would be: 

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