Is it true that Karp's work made all hard problems impossible?
Not at all. My work didn't make problems impossible; rather, it categorized their difficulty. The establishment of NP-completeness highlights which problems are likely to resist efficient, exact solutions using algorithms with polynomial running times. This understanding is crucial. It directs efforts towards developing practical approximations or heuristics for these problems, rather than wasting resources searching for a mythical efficient exact algorithm that likely doesn't exist. It's about understanding limits and finding the best possible approaches.
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