  This paper proposes a new class of simple, distributed algorithms for
scheduling in wireless networks. The algorithms generate new schedules in a
distributed manner via simple local changes to existing schedules. The class is
parameterized by integers $k\geq 1$. We show that algorithm $k$ of our class
achieves $k/(k+2)$ of the capacity region, for every $k\geq 1$. The algorithms
have small and constant worst-case overheads: in particular, algorithm $k$
generates a new schedule using {\em (a)} time less than $4k+2$ round-trip times
between neighboring nodes in the network, and {\em (b)} at most three control
transmissions by any given node, for any $k$. The control signals are
explicitly specified, and face the same interference effects as normal data
transmissions. Our class of distributed wireless scheduling algorithms are the
first ones guaranteed to achieve any fixed fraction of the capacity region
while using small and constant overheads that do not scale with network size.
The parameter $k$ explicitly captures the tradeoff between control overhead and
scheduler throughput performance and provides a tuning knob protocol designers
can use to harness this trade-off in practice.
