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In this work, we first propose a parallel batch switching algorithm called Small-Batch Queue-Proportional Sampling (SB-QPS). Compared to other batch switching algorithms, SB-QPS significantly reduces the batch size without sacrificing the throughput performance and hence has much lower delay when traffic load is light to moderate. It also achieves the lowest possible time complexity of O(1) per matching computation per port, via parallelization. We then propose another algorithm called Sliding-Window QPS (SW-QPS). SW-QPS retains and enhances all benefits of SB-QPS, and reduces the batching delay to zero via a novel switching framework called sliding-window switching. In addition, SW-QPS computes matchings of much higher qualities, as measured by the resulting throughput and delay performances, than QPS-1, the state-of-the-art regular switching algorithm that builds upon the same underlying bipartite matching algorithm. 

Set reconciliation is a fundamental algorithmic problem that arises in many networking, system, and database applications. In this problem, two large sets A and B of objects (bitcoins, files, records, etc.) are stored respectively at two different network-connected hosts, which we name Alice and Bob respectively. Alice and Bob communicate with each other to learn A Δ B , the difference between A and B , and as a result the reconciled set A ∪ B. Current set reconciliation schemes are based on either invertible Bloom filters (IBF) or error-correction codes (ECC). The former has a low computational complexity of O(d) , where d is the cardinality of A Δ B , but has a high communication overhead that is several times larger than the theoretical minimum. The latter has a low communication overhead close to the theoretical minimum, but has a much higher computational complexity of O(d 2 ). In this work, we propose Parity Bitmap Sketch (PBS), an ECC-based set reconciliation scheme that gets the better of both worlds: PBS has both a low computational complexity of O(d) just like IBF-based solutions and a low communication overhead of roughly twice the theoretical minimum. A separate contribution of this work is a novel rigorous analytical framework that can be used for the precise calculation of various performance metrics and for the near-optimal parameter tuning of PBS. 

In an input-queued switch, a crossbar schedule, or a matching between the input ports and the output ports needs to be computed for each switching cycle, or time slot. It is a challenging research problem to design switching algorithms that produce high-quality matchings yet have a very low computational complexity when the switch has a large number of ports. Indeed, there appears to be a fundamental tradeoff between the computational complexity of the switching algorithm and the quality of the computed matchings. Parallel maximal matching algorithms (adapted for switching) appear to be a sweet tradeoff point in this regard. On one hand, they provide the following performance guarantees: Using maxi- mal matchings as crossbar schedules results in at least 50% switch throughput and order-optimal (i.e., independent of the switch size 𝑁 ) average delay bounds for various traffic arrival processes. On the other hand, their computational complexities can be as low as 𝑂 (log_2 𝑁) per port/processor, which is much lower than those of the algorithms for finding matchings of higher qualities such as maximum weighted matching. In this work, we propose QPS-r, a parallel iterative switching algorithm that has the lowest possible computational complexity: 𝑂(1) per port. Yet, the matchings that QPS-r computes have the same quality as maximal matchings in the following sense: Using such matchings as crossbar schedules results in exactly the same aforementioned provable throughput and delay guarantees as using maximal matchings, as we show using Lyapunov stability analysis. Although QPS-r builds upon an existing add-on technique called Queue-Proportional Sampling (QPS), we are the first to discover and prove this nice property of such matchings. We also demon- strate that QPS-3 (running 3 iterations) has comparable empirical throughput and delay performances as iSLIP (running log 𝑁 itera- 2 tions), a refined and optimized representative maximal matching algorithm adapted for switching. 

In an input-queued switch, a crossbar schedule, or a matching between the input ports and the output ports needs to be computed for each switching cycle, or time slot. It is a challenging research problem to design switching algorithms that produce high-quality matchings yet have a very low computational complexity when the switch has a large number of ports. Indeed, there appears to be a fundamental tradeoff between the computational complexity of the switching algorithm and the quality of the computed matchings. Parallel maximal matching algorithms (adapted for switching) appear to be a sweet tradeoff point in this regard. On one hand, they provide the following performance guarantees: Using maxi- mal matchings as crossbar schedules results in at least 50% switch throughput and order-optimal (i.e., independent of the switch size 𝑁 ) average delay bounds for various traffic arrival processes. On the other hand, their computational complexities can be as low as 𝑂 (log2 𝑁 ) per port/processor, which is much lower than those of the algorithms for finding matchings of higher qualities such as maximum weighted matching. In this work, we propose QPS-r, a parallel iterative switching algorithm that has the lowest possible computational complexity: 𝑂(1) per port. Yet, the matchings that QPS-r computes have the same quality as maximal matchings in the following sense: Using such matchings as crossbar schedules results in exactly the same aforementioned provable throughput and delay guarantees as using maximal matchings, as we show using Lyapunov stability analysis. Although QPS-r builds upon an existing add-on technique called Queue-Proportional Sampling (QPS), we are the first to discover and prove this nice property of such matchings. We also demon- strate that QPS-3 (running 3 iterations) has comparable empirical throughput and delay performances as iSLIP (running log 𝑁 itera- 2 tions), a refined and optimized representative maximal matching algorithm adapted for switching.