Timer-based mechanisms are often used to help a given (sink) node select the
best helper node among many available nodes. Specifically, a node transmits a
packet when its timer expires, and the timer value is a monotone non-increasing
function of its local suitability metric. The best node is selected
successfully if no other node's timer expires within a 'vulnerability' window
after its timer expiry, and so long as the sink can hear the available nodes.
In this paper, we show that the optimal metric-to-timer mapping that (i)
maximizes the probability of success or (ii) minimizes the average selection
time subject to a minimum constraint on the probability of success, maps the
metric into a set of discrete timer values. We specify, in closed-form, the
optimal scheme as a function of the maximum selection duration, the
vulnerability window, and the number of nodes. An asymptotic characterization
of the optimal scheme turns out to be elegant and insightful. For any
probability distribution function of the metric, the optimal scheme is
scalable, distributed, and performs much better than the popular inverse metric
timer mapping. It even compares favorably with splitting-based selection, when
the latter's feedback overhead is accounted for.