请高手给翻译一篇英语文章,我的分不多,但是希望高手可以好心帮忙吧Abstract：Wepresentashortgeometricproofforthepriceofanar-chyresultsthathaverecentlybeenestablishedinaseriesofpapersonselfishroutingi

Question

请高手给翻译一篇英语文章,我的分不多,但是希望高手可以好心帮忙吧
Abstract： We present a short geometric proof for the price of anar-
chy results that have recently been established in a series of papers on
selfish routing in multicommodity flow networks. This novel proof also
facilitates two new types of results: On the one hand, we give pseudo-
approximation results that depend on the class of allowable cost func-
tions. On the other hand, we derive improved bounds on the inefficiency
of Nash equilibria for situations in which the equilibrium travel times
are within reasonable limits of the free-flow travel times. These tighter
bounds help to explain empirical observations in vehicular traffic net-
works. Our analysis holds in the more general context of congestion
games, which provides the framework in which we describe this work.

Answer 1

文摘:提出了一短的价格几何证明防线-
chy结果,最近成立于一系列的文件放在上面
自私multicommodity路由在流网络.这本小说也证明
促进两种新型结果:一方面,我们给伪-
近似结果,依靠这类允许成本func -
对其.另一方面,我们得到改善的低效率下界
平衡-纳什均衡的情况,对运行时间
是在合理的限度内的free-flow运行时间.这些紧缩
界限在经验主义的观察有助于解释进球,不准通车
作品.我们的分析中占据更一般的背景下堵塞