Smoothed Analysis of Inconsistent A*
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The paper investigates how algorithms for hard combinatorial optimization problems converge to trivial solutions, focusing on finite-size behavior rather than asymptotic limits. By analyzing large-graph asymptotics and running numerical experiments on problems like maximum independent set and maximum K‑SAT, the authors show that convergence to theoretically predicted bounds is surprisingly slow. In the intermediate regime of high constraint density, local algorithms actually outperform their asymptotic predictions, highlighting a gap between finite-regime performance and asymptotic theory.
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The paper investigates how optimization algorithms for hard combinatorial problems converge to trivial solutions. By combining rigorous large‑graph asymptotics with numerical experiments on maximum independent set and maximum K‑SAT, the authors show that convergence to the theoretically predicted bounds is extremely slow, especially in the intermediate regime of high constraint density. This reveals a significant gap between finite‑size performance and asymptotic expectations, indicating that practical algorithm design remains essential even when theory predicts inevitable failure.
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