distributed - A leader election algorithm for an oriented hypercube -

I am having some problem where I have to prepare a leader election algorithm for the oriented hypervisible. This should be done using tournaments with rounds equal to the dimension D of the hypervubube. In each step, 1 & lt; = D & lt; D neighbors of two dimensional Hyperkubes leaders (D + 1) - should compete to become a single candidate leader of Demental Hyperbolic, which is a union of their respective hypercubes. Problem: The problem is that as long as I study distributed systems, with a tolopogy in a network. In this topology, in every node, DD neighbors (where de is the dimension of hypervisome) is. Since the hypercube is oriented , nodes know what is the relation between each of their episodes with each dimension. Apart from this, I believe all the nodes are labeled with specific IDs, such as with these types of problems.

If I understand your solution guidelines well, the algorithm seems simple: OK D State in a node. Each state has 1 & lt; = D & lt; = D communicates with your neighbor with D axis. In this communication, the best candidate has to send the ID of which he is aware about (when D = 1 it is only his ID), and the ID obtained by PIR Compare it with Now the node knows the best ID of the sub-cube of order D (defined by excise 1,2 ..., D) it is related, thus, all nodes in Phase D are aware of the global best, and the algorithm is complete with an unanimous it happens. For example, consider the following topology (D = 2) and id values:

  (1) (2) 1 ----- 2 | | | | 4 ----- 3 (4) (3)  

ID in parentheses so far notify the best IDs known by each node.

The first iteration (D = 1) works with the horizontal axis, and ends as follows:

  (2) (2) 1---- - 2 | | | | 4 ----- 3 (4) (4)  

The second (and last) walk (D = 2) works with the vertical axis, and ends as follows:

(4) (4) 1 ----- 2 | | | | 4 ----- 3 (4) (4)

The node number 4 has been selected as required (highest id).

Message count complexity

We have exactly 2 messages for each edge in the hyperview (one in each direction). The formula for the number of edges in the hypervisap of the dimension D is E = D * 2 ^ (D-1), so we have exactly M = D * 2 ^ D messages as an function of I n (number of nodes) To calculate complexity, remember that N = 2 ^ D, then M = N * log n.