Before revision:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries such as barcodes and distances among them cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.
After revision:  However, in the multi-parameter setting, one of the main bottlenecks is that topological summaries based on algebraic structure such as decompositions and bottleneck distances cannot be as efficiently computed as in the 1-parameter case because there is no known generalization of the persistence algorithm for computing the decomposition of multi-parameter persistence modules.