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桑杰夫·阿羅拉近似算法的理論突破

桑杰夫·阿羅拉因在近似算法理論方面的突破性工作而獲得哥德爾獎(jiǎng)。他的研究為解決NP難問題提供了新的視角和方法，對(duì)算法設(shè)計(jì)有重要貢獻(xiàn)。

理解計(jì)算的極限與擴(kuò)展其能力同樣重要。

"Understanding the limits of computation is as important as expanding its capabilities."

桑杰夫·阿羅拉

"Understanding the limits of computation is as important as expanding its capabilities."

理解計(jì)算的極限與擴(kuò)展其能力同樣重要。

桑杰夫·阿羅拉

計(jì)算機(jī)科學(xué)中理論與實(shí)踐之間的相互作用是推動(dòng)該領(lǐng)域前進(jìn)的動(dòng)力。

"The interplay between theory and practice in computer science is what drives the field forward."

桑杰夫·阿羅拉

"The interplay between theory and practice in computer science is what drives the field forward."

計(jì)算機(jī)科學(xué)中理論與實(shí)踐之間的相互作用是推動(dòng)該領(lǐng)域前進(jìn)的動(dòng)力。

桑杰夫·阿羅拉

在計(jì)算復(fù)雜性的研究中，我們常常發(fā)現(xiàn)可能的邊界是由我們想象力的極限定義的。

"In the study of computational complexity, we often find that the boundaries of what is possible are defined by the limits of our imagination."

桑杰夫·阿羅拉

"In the study of computational complexity, we often find that the boundaries of what is possible are defined by the limits of our imagination."

在計(jì)算復(fù)雜性的研究中，我們常常發(fā)現(xiàn)可能的邊界是由我們想象力的極限定義的。

桑杰夫·阿羅拉

理論洞察可以帶來(lái)實(shí)際突破，彌合抽象思想與現(xiàn)實(shí)應(yīng)用之間的差距。

"Theoretical insights can lead to practical breakthroughs, bridging the gap between abstract ideas and real-world applications."

桑杰夫·阿羅拉

"Theoretical insights can lead to practical breakthroughs, bridging the gap between abstract ideas and real-world applications."

理論洞察可以帶來(lái)實(shí)際突破，彌合抽象思想與現(xiàn)實(shí)應(yīng)用之間的差距。

桑杰夫·阿羅拉

算法的創(chuàng)新往往來(lái)自于以新的方式看待舊問題。

"Innovation in algorithms often comes from looking at old problems in new ways."

桑杰夫·阿羅拉

"Innovation in algorithms often comes from looking at old problems in new ways."

算法的創(chuàng)新往往來(lái)自于以新的方式看待舊問題。

桑杰夫·阿羅拉

在計(jì)算機(jī)科學(xué)中追求知識(shí)，是在無(wú)限可能性的風(fēng)景中旅行。

"The pursuit of knowledge in computer science is a journey through a landscape of infinite possibilities."

桑杰夫·阿羅拉

"The pursuit of knowledge in computer science is a journey through a landscape of infinite possibilities."

在計(jì)算機(jī)科學(xué)中追求知識(shí)，是在無(wú)限可能性的風(fēng)景中旅行。

桑杰夫·阿羅拉

復(fù)雜性理論告訴我們，并非所有問題都是平等的；有些問題本質(zhì)上比其他問題更難。

"Complexity theory teaches us that not all problems are created equal; some are inherently harder than others."

桑杰夫·阿羅拉

"Complexity theory teaches us that not all problems are created equal; some are inherently harder than others."

復(fù)雜性理論告訴我們，并非所有問題都是平等的；有些問題本質(zhì)上比其他問題更難。

桑杰夫·阿羅拉

計(jì)算機(jī)科學(xué)中數(shù)學(xué)的美在于它能夠用抽象概念建模和解決現(xiàn)實(shí)世界的問題。

"The beauty of mathematics in computer science lies in its ability to model and solve real-world problems with abstract concepts."

桑杰夫·阿羅拉

"The beauty of mathematics in computer science lies in its ability to model and solve real-world problems with abstract concepts."

計(jì)算機(jī)科學(xué)中數(shù)學(xué)的美在于它能夠用抽象概念建模和解決現(xiàn)實(shí)世界的問題。

桑杰夫·阿羅拉

在算法的領(lǐng)域，優(yōu)雅不僅僅是美學(xué)；它常常帶來(lái)效率。

"In the realm of algorithms, elegance is not just aesthetic; it often leads to efficiency."

桑杰夫·阿羅拉

"In the realm of algorithms, elegance is not just aesthetic; it often leads to efficiency."

在算法的領(lǐng)域，優(yōu)雅不僅僅是美學(xué)；它常常帶來(lái)效率。

桑杰夫·阿羅拉

理論計(jì)算機(jī)科學(xué)不僅僅是解決問題，更是理解計(jì)算本身的本質(zhì)。

"Theoretical computer science is not just about solving problems, but about understanding the nature of computation itself."

桑杰夫·阿羅拉

"Theoretical computer science is not just about solving problems, but about understanding the nature of computation itself."

理論計(jì)算機(jī)科學(xué)不僅僅是解決問題，更是理解計(jì)算本身的本質(zhì)。

桑杰夫·阿羅拉

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