Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
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In a network of asynchronous processors, the cost to send a message can differ significantly from one communication link to another. In such a setting, it is desirable to factor the cost of links into the cost of distributed computation. Assume that associated with each link is a positive weight representing the cost of sending one message along the link, and the cost of an algorithm executed on a weighted network is the sum of the costs of all messages sent during its execution. We determine the asymptotic complexity of distributed leader election on a weighted unidirectional asynchronous ring assuming this notion of cost, by exhibiting a simple algorithm and a matching lower bound for the problem for any collection of edge weights. As a consequence, we see that algorithms designed for unweighted rings are not in general efficient for the weighted case.