Parallel maximum weight bipartite matching algorithms for scheduling in input-queued switches

Summary form only given. An input-queued switch with virtual output queuing is able to provide a maximum throughput of 100% in the supporting more sophisticated scheduling strategies. Switch scheduling can be cast as a maximum flow problem. We propose a maximum weight bipartite matching (MWBM) scheduling algorithm for input-queued switches. Our goal is to provide 100% throughput while maintaining fairness and stability. Our algorithm provides sublinear parallel run time complexity using a polynomial number of processing elements. We are able to obtain the MWBM for a time slot in sublinear time by using the matching produced in the previous time slot based on the observation that in input-queued cell-based switches, the weight of edges changes very little during successive time slots. To the best of our knowledge, our algorithm outperforms all previously proposed MWBM scheduling algorithms proposed for input-queued switches. We also describe a linear time complexity MWBM algorithm for a general bipartite graph which outperforms the best known sublinear MWBM algorithm for any bipartite graph with less than 10¹⁵ number of nodes.