This paper concerns computing approximate pure Nash equilibria in weighted congestion games, which has been shown to be PLS-complete. With the help of $\hat{\Psi}$-game and approximate potential functions, we propose two algorithms based on best response dynamics, and prove that they efficiently compute $\frac{\rho}{1-\epsilon}$-approximate pure Nash equilibria for $\rho= d!$ and $\rho =\frac{2\cdot W\cdot(d+1)}{2\cdot W+d+1}\le {d + 1}$, respectively, when the weighted congestion game has polynomial latency functions of degree at most $d \ge 1$ and players' weights are bounded from above by a constant $W \ge 1$. This improves the recent work of Feldotto et al.[2017] and Giannakopoulos et al. [2022] that showed efficient algorithms for computing $d^{d+o(d)}$-approximate pure Nash equilibria.

翻译：本文涉及在加权拥堵游戏中计算近乎纯净纳什平衡的纯纳什平衡( 已证明是PLS) 。 在$\hat=Psi}$game 和近似潜在功能的帮助下, 我们提出基于最佳反应动态的两种算法, 并证明它们以$\rho= d. 和$\rho= d. 和$\rtoto et al. [2017] 和 Gianankopoulos et al. [2022] 的近期工作得到了改进,这些算法显示了计算 $d+d+o( d) $- pal equilia 的有效算法。