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We consider the problem of enumerating optimal solutions for two hypergraph k-partitioning problems, namely, Hypergraph-k-Cut and Minmax-Hypergraph-k-Partition. The input in hypergraph k-partitioning problems is a hypergraph [Formula: see text] with positive hyperedge costs along with a fixed positive integer k. The goal is to find a partition of V into k nonempty parts [Formula: see text]—known as a k-partition—so as to minimize an objective of interest. (1) If the objective of interest is the maximum cut value of the parts, then the problem is known as Minmax-Hypergraph-k-Partition. A subset of hyperedges is a minmax-k-cut-set if it is the subset of hyperedges crossing an optimum k-partition for Minmax-Hypergraph-k-Partition. (2) If the objective of interest is the total cost of hyperedges crossing the k-partition, then the problem is known as Hypergraph-k-Cut. A subset of hyperedges is a min-k-cut-set if it is the subset of hyperedges crossing an optimum k-partition for Hypergraph-k-Cut. We give the first polynomial bound on the number of minmax-k-cut-sets and a polynomial-time algorithm to enumerate all of them in hypergraphs for every fixed k. Our technique is strong enough to also enable an [Formula: see text]-time deterministic algorithm to enumerate all min-k-cut-sets in hypergraphs, thus improving on the previously known [Formula: see text]-time deterministic algorithm, in which n is the number of vertices and p is the size of the hypergraph. The correctness analysis of our enumeration approach relies on a structural result that is a strong and unifying generalization of known structural results for Hypergraph-k-Cut and Minmax-Hypergraph-k-Partition. We believe that our structural result is likely to be of independent interest in the theory of hypergraphs (and graphs). Funding: All authors were supported by NSF AF 1814613 and 1907937. 

Digital content services provide users with a wide range of content, such as news, articles, or movies, while monetizing their content through various business models and promotional methods. Unfortunately, poorly designed or unpro- tected business logic can be circumvented by malicious users, which is known as business flow tampering. Such flaws can severely harm the businesses of digital content service providers. In this paper, we propose an automated approach that discov- ers business flow tampering flaws. Our technique automatically runs a web service to cover different business flows (e.g., a news website with vs. without a subscription paywall) to collect execution traces. We perform differential analysis on the execution traces to identify divergence points that determine how the business flow begins to differ, and then we test to see if the divergence points can be tampered with. We assess our approach against 352 real-world digital content service providers and discover 315 flaws from 204 websites, including TIME, Fortune, and Forbes. Our evaluation result shows that our technique successfully identifies these flaws with low false-positive and false- negative rates of 0.49% and 1.44%, respectively.