Approximations to maximum weight matching scheduling algorithms of low complexity

The choice of the scheduling algorithm is a major design criterion of a switch. Whereas it is known that maximum weight matching algorithms guarantee the stability of an input-queued switch, their computational complexity does not allow their practical deployment. In consequence, researchers have designed scheduling algorithms of low complexity and with satisfying performance features. We extend this field of research by investigating the application of matching algorithms of low complexity that approximate maximum weight matching algorithms as scheduling algorithms for input-queued switches. We prove that an algorithm that approximates a maximum weight matching algorithm with approximation parameters (c, d), stabilizes a combined input/output-queued switch with a speed-up of 1/c. As an application, we show that four known scheduling algorithms of low complexity stabilize a combined input/output-queued switch with a speed-up of two. Finally, we prove that the improve_matching algorithm can stabilize an input-queued switch when it is deployed with a speed-up of (3/2)+ε.