https://cs.lozic.me/areas/optimization/Recent content in Optimization on CS TheoremsHugoen-usFri, 14 May 2027 12:00:00 +0100https://cs.lozic.me/posts/t032-approximation-algorithms-and-ratios/Fri, 14 May 2027 12:00:00 +0100https://cs.lozic.me/posts/t032-approximation-algorithms-and-ratios/<h2 id="symptom">Symptom</h2> <p>You have accepted that the problem is NP-hard. Now what?</p> <p>The literature offers a wall of results with numbers attached: 2-approximation, $\ln n$-approximation, PTAS, FPTAS, 0.878. Nobody explains what these numbers buy you, how they are proved, or how they connect to the heuristic you already wrote. Meanwhile your greedy heuristic is running in production and you have no idea whether it is within 5% or a factor of 50 of optimal, because <strong>you cannot compute the optimum to compare against</strong> — that was the whole problem.</p>