Efficient Detection of Long Consistent Cycles and its Application to Distributed Synchronization
Authors: Shaohan Li, Yunpeng Shi, Gilad Lerman

Group synchronization plays a crucial role in global pipelines for Structure from Motion (SfM). Its formulation is nonconvex and it is faced with highly corrupted measurements. Cycle consistency has been effective in addressing these challenges. However computationally efficient solutions are needed for cycles longer than three especially in practical scenarios where 3-cycles are unavailable. To overcome this computational bottleneck we propose an algorithm for group synchronization that leverages information from cycles of lengths ranging from three to six with a complexity of O(n^3) (or O(n^ 2.373 ) when using a faster matrix multiplication algorithm). We establish non-trivial theory for this and related methods that achieves competitive sample complexity assuming the uniform corruption model. To advocate the practical need for our method we consider distributed group synchronization which requires at least 4-cycles and we illustrate state-of-the-art performance by our method in this context.