  We consider a set of transmitter-receiver pairs, or links, that share a
common channel and address the problem of emptying backlogged queues at the
transmitters in minimum time. The problem amounts to determining activation
subsets of links and their time durations to form a minimum-length schedule.
The problem of scheduling has been studied under various formulations before.
In this paper, we present fundamental insights and solution characterizations
that include: (i) showing that the complexity of the problem remains high for
any continuous and increasing rate function, (ii) formulating and proving
sufficient and necessary optimality conditions of two base scheduling
strategies that correspond to emptying the queues using "one-at-a-time" or
"all-at-once" strategies, (iii) presenting and proving the tractability of the
special case in which the transmission rates are functions only of the
cardinality of the link activation sets. These results are independent of
physical-layer system specifications and are valid for any form of rate
function. We then develop an algorithmic framework. The framework encompasses
exact as well as sub-optimal, but fast, scheduling algorithms, all under a
unified principle design. Through computational experiments we finally
investigate the performance of several specific algorithms.
