We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay O(m k * +1 • n 2 ) and uses linear space. Hereby, n is the number of vertices, m the number of hyperedges, and k * the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality k * of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W [3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations.

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Assigning staff to engagements according to hard constraints while optimizing several objectives is a task encountered by many companies on a regular basis. Simplified versions of such assignment problems are NP-hard. Despite this, a typical approach to solving them consists of formulating them as mixed integer programming (MIP) problems and using a stateof-the-art solver to get solutions that closely approximate the optimum.In this paper, we consider a complex real-world staff assignment problem encountered by the professional service company KPMG, with the goal of finding an algorithm that solves it faster and with a better solution than a commercial MIP solver. We follow the evolutionary algorithm (EA) metaheuristic and design a search heuristic which iteratively improves a solution using domain-specific mutation operators. Furthermore, we use a flow algorithm to optimally solve a subproblem, which tremendously reduces the search space for the EA.For our real-world instance of the assignment problem, given the same total time budget of 100 hours, a parallel EA approach finds a solution that is only 1.7% away from an upper bound for the (unknown) optimum within under five hours, while the MIP solver Gurobi still has a gap of 10.5%.

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