The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to solve hitting set. Though it requires exponential time in the worst case, it can solve many practical instances from different domains in reasonable time. Our algorithm outperforms a modern ILP solver, the state-of-the-art for hitting set, by at least an order of magnitude on most instances.
翻译:点击设置问题要求收集宇宙各组的一组美元, 以寻找每个特定组的最小子集( $U ) 。 它是NP 硬的, 与问题套套套相等 。 我们给分支和约束算法来解击套套。 虽然最坏的则需要指数化时间, 但它可以在合理的时间内解决不同域的许多实际案例 。 我们的算法优于现代的 ILP 求解器, 即最先进的击球技术, 多数情况下至少要达到一个数量级 。