A Master of the Traveling Salesperson Problem Finds His Own Path
For Shayan Oveis Gharan, progress on hard problems often comes via unexpected detours.
对于 Shayan Oveis Gharan 来说，解决难题的进展往往是通过意想不到的弯路来实现的。
I n theoretical computer science, the key to cracking tough problems is finding the right tools.
在理论计算机科学中，解决棘手问题的关键是找到合适的工具。
Most researchers gravitate toward tools that match the problems they hope to solve, and some devote entire careers to mastering a few familiar techniques.
大多数研究人员倾向于使用与他们希望解决的问题相匹配的工具，有些研究人员将整个职业生涯都奉献给掌握一些熟悉的技术。
But Shayan Oveis Gharan , a computer scientist at the University of Washington in Seattle, has never been content with the familiar.
但西雅图华盛顿大学计算机科学家 Shayan Oveis Gharan 从来不满足于熟悉的事物。
When he sticks with the same approach for too long, he gets restless.
当他长时间坚持同一种方法时，他就会变得焦躁不安。
“I’m not learning anything new,” he said.
“我没有学到任何新东西，”他说。
“I’m just sort of staying where I am.”
“我只是呆在原地。”
Physically as well as intellectually, Oveis Gharan seems to have trouble staying still.
无论是身体上还是智力上，奥韦斯·加兰似乎都很难保持静止。
Talk to him about his research, and he’ll grow increasingly animated, shifting constantly from one unorthodox position to another — first sitting cross-legged in an armchair, then hugging his knees to his chest, then turning sideways and draping his legs over the armrest.
和他谈论他的研究，他会变得越来越活跃，不断地从一种非正统的姿势变换到另一种姿势——首先盘腿坐在扶手椅上，然后将膝盖抱在胸前，然后转向一侧，将双腿搭在扶手上。
Perhaps it’s fitting, then, that Oveis Gharan is renowned for his work on the traveling salesperson problem, a notoriously difficult computational problem about roaming from place to place.
那么，奥韦斯·加兰 (Oveis Gharan) 因其在旅行推销员问题上的研究而闻名，这是一个众所周知的关于从一个地方漫游到另一个地方的困难计算问题，这也许是合适的。
He’s also made major contributions to a seemingly unrelated subject: understanding the best way to choose randomly from a large collection of mathematical objects.
他还对一个看似无关的主题做出了重大贡献：了解从大量数学对象中随机选择的最佳方法。
For these efforts and others, Oveis Gharan has received the International Mathematical Union’s Abacus Medal, awarded every four years to a theoretical computer scientist under 40.
由于这些努力和其他努力，Oveis Gharan 获得了国际数学联盟的珠算奖章，该奖章每四年颁发给一位 40 岁以下的理论计算机科学家。
The award committee cited his use of novel tools from far-flung reaches of mathematics that appear unrelated to computer science.
颁奖委员会提到了他使用了来自遥远数学领域的新颖工具，这些工具似乎与计算机科学无关。
It’s as if a creative carpenter discovered that for some tasks a stethoscope works better than a saw.
就好像一位富有创造力的木匠发现，对于某些任务来说，听诊器比锯子更有效。
“This is what a lot of the brilliant, great researchers do,” said Anna Karlin , a colleague and collaborator of Oveis Gharan’s at the University of Washington.
“这就是许多才华横溢、伟大的研究人员所做的事情，”华盛顿大学奥维斯·加兰的同事兼合作者安娜·卡林 (Anna Karlin) 说。
“They connect things that are seemingly disconnected.”
“它们将看似互不相关的事物联系起来。”
Oveis Gharan is known for his energy and enthusiasm.
奥韦斯·加兰 (Oveis Gharan) 以其精力和热情而闻名。
“He’s incredibly fun to work with,” said his colleague Anna Karlin.
“和他一起工作非常有趣，”他的同事安娜·卡林说。
“He’s a believer that you can make progress.”
“他相信你可以取得进步。”
Researchers who draw connections between disparate fields often cultivate their breadth of knowledge at the expense of deep engagement with any one subject.
在不同领域之间建立联系的研究人员常常以牺牲对某一学科的深入参与为代价来培养知识的广度。
But not Oveis Gharan.
但奥韦斯·加兰不是。
For all his restless energy, he has the patience to sit with hard problems for years and attend to every technical detail of a long and complex proof.
尽管他精力充沛，但他有耐心多年解决难题，并关注冗长而复杂的证明的每一个技术细节。
“Shayan can kind of do it all,” said Jonathan Leake , a mathematician at the University of Waterloo who collaborates with Oveis Gharan.
“Shayan 可以做到这一切，”与 Oveis Gharan 合作的滑铁卢大学数学家 Jonathan Leake 说。
“I don’t know how he does it, honestly.”
“老实说，我不知道他是怎么做到的。”
Oveis Gharan’s chosen field of theoretical computer science centers on understanding algorithms, the mathematical procedures that computers use to accomplish specific tasks.
奥维斯·加兰 (Oveis Gharan) 选择的理论计算机科学领域以理解算法为中心，即计算机用来完成特定任务的数学过程。
Some researchers seek to map the limits of computation, by identifying problems that are too hard for even the cleverest algorithms.
一些研究人员试图通过识别即使是最聪明的算法也难以解决的问题来绘制计算的极限。
Others aim to push the boundaries of what algorithms can do.
其他人则致力于突破算法的界限。
Oveis Gharan, an optimist at heart, falls squarely in the latter group.
奥韦斯·加兰 (Oveis Gharan) 本质上是个乐观主义者，他恰好属于后者。
“I’m on the positive side,” he said.
“我持积极的一面，”他说。
“I like to say things are possible.”
“我喜欢说一切皆有可能。”
Oveis Gharan is slender and sprightly, with unruly black hair and an irrepressible smile.
奥韦斯·加兰 (Oveis Gharan) 身材修长，精神抖擞，一头不羁的黑发，脸上挂着难以抑制的微笑。
His enthusiasm for his work is palpable, even infectious.
他对工作的热情是显而易见的，甚至具有感染力。
“He’s incredibly fun to work with,” Karlin said.
“和他一起工作非常有趣，”卡林说。
“He’s a believer that you can make progress.”
“他相信你可以取得进步。”
Shayan Oveis Gharan has never been content with the familiar.
Shayan Oveis Gharan 从来不满足于熟悉的事物。
When he sticks with the same approach for too long, he gets restless.
当他长时间坚持同一种方法时，他就会变得焦躁不安。
Recent events outside mathematics have tested Oveis Gharan’s characteristic optimism.
最近数学以外的事件考验了奥韦斯·加兰特有的乐观态度。
In the past 12 months alone, his fellow Iranians have endured a violent crackdown on protests by their government; a raft of punitive economic sanctions imposed by the United States, the European Union, and the United Nations; and airstrikes by the U.S. and Israel whose targets included Sharif University of Technology in Tehran, Iran’s leading science and engineering school and Oveis Gharan’s alma mater.
仅在过去 12 个月里，他的伊朗同胞就遭受了政府对抗议活动的暴力镇压。美国、欧盟和联合国实施的一系列惩罚性经济制裁；美国和以色列的空袭目标包括德黑兰谢里夫理工大学，伊朗领先的科学与工程学校，也是奥韦斯·加兰的母校。
“I see a lot of my old friends and family members suffering,” he said.
“我看到很多老朋友和家人正在遭受痛苦，”他说。
“It gets hard to work.”
“工作变得很困难。”
Oveis Gharan was born in the historic city of Isfahan in 1986 during another difficult time in his country’s history — the eight-year war with Iraq.
1986 年，奥韦斯·加兰 (Oveis Gharan) 出生于历史名城伊斯法罕，当时正值该国历史上的另一个困难时期——与伊拉克的八年战争。
His father was a civil engineer, and his mother, Fatemeh Khoei, was a middle-school biology teacher who earlier in life had reluctantly set aside her aspirations to study mathematics.
他的父亲是一名土木工程师，母亲法特梅·科伊 (Fatemeh Khoei) 是一名中学生物老师，她早年曾不情愿地放弃了学习数学的愿望。
“At the time she was growing up, the culture was ‘girls should not get into math,’” Oveis Gharan said.
“在她成长的过程中，文化是‘女孩不应该学习数学’，”奥维斯·加兰说。
“She didn’t have the opportunity.”
“她没有机会。”
Instead, Khoei pushed her children to excel academically.
相反，科伊督促她的孩子们在学业上取得优异成绩。
Shayan was the youngest of five.
沙彦是五个孩子中最小的一个。
He grew up watching his siblings, who range in age from six to 13 years older than he is, studying math, science, and medicine.
他是看着年龄比他大 6 岁到 13 岁的兄弟姐妹学习数学、科学和医学长大的。
As a boy, he was shy but had a competitive streak, and he was eager to prove that he could match his talented siblings’ accomplishments.
作为一个男孩，他很害羞，但具有竞争性，他渴望证明自己可以与他才华横溢的兄弟姐妹的成就相媲美。
“He was always comparing himself with older kids,” Khoei said in Farsi as her daughter Shadi translated.
“他总是把自己与年龄较大的孩子进行比较，”科伊用波斯语说道，她的女儿莎迪负责翻译。
Oveis Gharan is an optimist at heart.
奥韦斯·加兰 (Oveis Gharan) 本质上是一位乐观主义者。
“I’m on the positive side,” he said.
“我持积极的一面，”他说。
“I like to say things are possible.”
“我喜欢说一切皆有可能。”
Shayan was especially close to his brother Shahab, who studied computer science and competed in the International Olympiad in Informatics, a contest of math and programming skill, in the late 1990s.
Shayan 与他的兄弟 Shahab 关系特别密切，Shahab 学习计算机科学，并参加了 20 世纪 90 年代末的国际信息学奥林匹克竞赛，这是一项数学和编程技能的竞赛。
When Shayan started middle school, Shahab gave him a book of math puzzles, and he was instantly hooked.
当 Shayan 开始上中学时，Shahab 给了他一本数学谜题书，他立刻就着迷了。
“It brought a sparkle to his mind to dig much, much deeper,” Shahab recalled.
沙哈布回忆道：“这让他的头脑焕发出了一种火花，让他能够更加深入地挖掘。”
Shayan went on to compete in the Olympiad himself and won a gold medal in 2004.
Shayan 随后参加了奥林匹克运动会并于 2004 年获得金牌。
Though it was the mathematical side of computer science that initially drew him to the field, Oveis Gharan studied computer engineering as an undergraduate at Sharif University, thinking it would offer a more stable career.
尽管最初吸引他进入该领域的是计算机科学的数学方面，但 Oveis Gharan 在谢里夫大学读本科时学习了计算机工程，认为这将提供更稳定的职业生涯。
In his first year, he began dating a fellow engineering student, Farnaz Ronaghi, and the two bonded over hikes in the mountains and wide-ranging conversations about philosophy and religion.
第一年，他开始与一位工程系学生法纳兹·罗纳吉(Farnaz Ronaghi)约会，两人通过山里徒步旅行以及有关哲学和宗教的广泛对话而结下不解之缘。
They married at the end of college and soon faced a big decision about their future.
他们在大学毕业后结婚，很快就面临着关于自己未来的重大决定。
Oveis Gharan, who’d found work in the computer graphics industry, was inclined to stay in Iran, but Ronaghi wanted to continue her education abroad, and she convinced him to apply to graduate school.
在计算机图形行业找到工作的奥韦斯·加兰 (Oveis Gharan) 倾向于留在伊朗，但罗纳吉 (Ronaghi) 想在国外继续学业，她说服他申请研究生院。
Both were admitted to Stanford University, where Oveis Gharan’s sister Shadi, the first in the family to emigrate, had just received her doctorate in electrical engineering.
两人都考入了斯坦福大学，奥韦斯·加兰的妹妹沙迪（Shadi）是家里第一个移民的人，刚刚获得了电气工程博士学位。
Shadi encouraged her still-reluctant brother to accept the offer — theoretical research would open new opportunities, she said, and he could always go back to a software job if he didn’t like it.
沙迪鼓励她仍然不情愿的哥哥接受这份工作——她说，理论研究会带来新的机会，如果他不喜欢，他随时可以回到软件工作。
As it happened, a taste of research was all that Oveis Gharan needed to rekindle his love of mathematics.
碰巧的是，奥韦斯·加兰（Oveis Gharan）只需要尝试一下研究就能重新点燃他对数学的热爱。
Graduate school was where Oveis Gharan first encountered the traveling salesperson problem, the famously thorny question that he would wrestle with on and off for the next decade.
研究生院是奥韦斯·加兰 (Oveis Gharan) 第一次遇到旅行推销员问题的地方，这是一个著名的棘手问题，他在接下来的十年里断断续续地与这个问题作斗争。
It asks: Given any map of cities connected by a road network, what is the shortest round-trip route that passes through every city?
它提出的问题是：给定任何由道路网络连接的城市地图，经过每个城市的最短往返路线是什么？
Researchers think there’s no way to design an algorithm that can quickly find the exact solution for all possible maps.
研究人员认为，没有办法设计一种算法可以快速找到所有可能地图的精确解决方案。
Instead, they aim to design algorithms that always find relatively short round-trip tours — reasonable approximations of the ideal route.
相反，他们的目标是设计能够始终找到相对较短的往返行程的算法——理想路线的合理近似值。
Oveis Gharan in his office at the University of Washington.
奥韦斯·加兰 (Oveis Gharan) 在华盛顿大学的办公室里。
In 1976, the mathematician Nicos Christofides devised a simple algorithm that yields a remarkably good approximation : It always finds a round-trip tour that’s at most 50% longer than the shortest possible route.
1976 年，数学家 Nicos Christofides 设计了一种简单的算法，可以产生非常好的近似值：它总是找到比最短路线最多长 50% 的往返旅行。
(In the Soviet Union, Anatoliy Serdyukov came up with the same idea independently around the same time.) Ever since then, researchers have tried in vain to craft an algorithm that’s guaranteed to get closer to the exact solution.
（在苏联，阿纳托利·谢尔久科夫（Anatoliy Serdyukov）大约在同一时间独立提出了相同的想法。）从那时起，研究人员一直徒劳地尝试制定一种保证更接近精确解决方案的算法。
In Oveis Gharan’s first year of graduate school, he helped his adviser Amin Saberi and other researchers design an algorithm for the “asymmetric” version of the traveling salesperson problem, in which maps can include one-way roads.
在 Oveis Gharan 读研究生的第一年，他帮助他的导师 Amin Saberi 和其他研究人员设计了一种算法，用于解决旅行推销员问题的“非对称”版本，其中地图可以包含单向道路。
Bolstered by that success, Oveis Gharan, Saberi, and the computer scientist Mohit Singh set out to prove that a similar method could beat Christofides’ record for the original symmetric problem.
受到这一成功的鼓舞，Oveis Gharan、Saberi 和计算机科学家 Mohit Singh 开始证明类似的方法可以打破 Christofides 解决原始对称问题的记录。
As a second-year graduate student, Oveis Gharan quickly took charge of the effort.
作为一名二年级研究生，奥韦斯·加兰 (Oveis Gharan) 很快就负责了这项工作。
Saberi was used to giving students feedback on their ideas, but in his meetings with Oveis Gharan, he often found himself on the receiving end.
萨贝里习惯于向学生提供有关他们想法的反馈，但在与奥韦斯·加兰的会面中，他经常发现自己处于接收端。
“In his own cheerful and polite way, [he’d] explain in the first 10 minutes of the meeting why the approach I suggested is unlikely to work,” Saberi said.
“他会在会议的前 10 分钟内以他自己愉快而礼貌的方式解释为什么我建议的方法不太可能奏效，”萨贝里说。
“Then for the other 15 minutes, we would be discussing what he thought would be the right way.”
“然后在另外 15 分钟里，我们将讨论他认为正确的方法。”
Researchers who study the traveling salesperson problem use mathematical representations of maps called graphs: networks in which nodes represent cities, and the links between them (called edges) represent roads.
研究旅行推销员问题的研究人员使用称为图的地图的数学表示：网络中的节点代表城市，节点之间的链接（称为边）代表道路。
The first step in many algorithms, including Christofides’, is to find a specific kind of path through the graph called a spanning tree, which touches every node but contains no closed loops.
许多算法（包括 Christofides 的算法）的第一步是在图中找到一种称为生成树的特定路径，它接触每个节点但不包含闭环。
Every graph has many possible spanning trees.
每个图都有许多可能的生成树。
Once you have a spanning tree, you can transform it into a round-trip route by adding edges or doubling back at dead ends.
一旦你有了生成树，你就可以通过添加边或在死胡同折返来将其转换为往返路线。
A key question for traveling salesperson algorithms is which of the many spanning-tree options to start with.
旅行推销员算法的一个关键问题是从众多生成树选项中的哪一个开始。
Christofides’ algorithm picks out the one that’s shortest when you add up the lengths of all its edges.
当你将所有边的长度相加时，Christofides 的算法会选出最短的一条。
This is usually a good starting point.
这通常是一个很好的起点。
But for some graphs, the shortest spanning tree has many dead-end branches, so the process of transforming it into a round-trip tour can actually make the route much longer.
但对于某些图来说，最短生成树有很多死胡同分支，因此将其转化为往返之旅的过程实际上可以使路线变得更长。
Oveis Gharan and his colleagues hoped to avoid these extra-long routes by first harnessing randomness to select a promising spanning tree, and then transforming it into a round-trip tour.
Oveis Gharan 和他的同事希望通过首先利用随机性来选择一棵有希望的生成树，然后将其转变为往返旅行，从而避免这些超长的路线。
Randomness had been the crucial ingredient in their algorithm for the asymmetric traveling salesperson problem, and they quickly worked out how to adapt that algorithm to the symmetric problem.
随机性是他们解决非对称旅行推销员问题的算法的关键因素，他们很快就找到了如何使该算法适应对称问题的方法。
They thought that this approach would be able to beat Christofides’ algorithm — intuitively, if you use randomness to choose a spanning tree, you won’t get stymied by cases where the shortest spanning tree turns out to be a bad choice.
他们认为这种方法能够击败 Christofides 的算法——直观地讲，如果你使用随机性来选择生成树，你就不会因为最短生成树被证明是一个糟糕的选择而受到阻碍。
The more randomness, the better.
随机性越多越好。
But turning this intuition into a rigorous proof was not easy.
但将这种直觉转化为严格的证明并不容易。
They needed a way to analyze mathematical expressions that specify the chance of getting each possible spanning tree.
他们需要一种方法来分析数学表达式，指定获得每个可能的生成树的机会。
Even a relatively small graph can have billions of spanning trees, and it’s hard to reason about problems with so many possibilities.
Even a relatively small graph can have billions of spanning trees, and it’s hard to reason about problems with so many possibilities.
The key was to transform those mathematical expressions into formulas called polynomials, in which variables are multiplied and added together.
关键是将这些数学表达式转换为称为多项式的公式，其中变量相乘并相加。
Rewriting the problem in this unusual form, with one added term for each possible spanning tree, allowed Oveis Gharan to analyze it with a new set of mathematical tools .
以这种不寻常的形式重写问题，为每个可能的生成树添加一个术语，使奥韦斯·加兰能够使用一组新的数学工具对其进行分析。
“Then you translate your finding to the setting of the original problem,” he said.
“Then you translate your finding to the setting of the original problem,” he said.
“It’s like a detour.”
“这就像是走了一条弯路。”
Armed with these new tools, Oveis Gharan and colleagues proved that their new algorithm outperformed Christofides’ classic algorithm for an important special case of the traveling salesperson problem.
借助这些新工具，Oveis Gharan 及其同事证明，对于旅行推销员问题的一个重要特例，他们的新算法优于 Christofides 的经典算法。
They suspected that there was more to the story — that the new algorithm would actually be superior in the most general case.
They suspected that there was more to the story — that the new algorithm would actually be superior in the most general case.
It would take a few more detours to prove it.
还需要多走一些弯路才能证明这一点。
Oveis Gharan’s early work on the traveling salesperson problem was the first instance of a pattern that would recur throughout his career.
奥韦斯·加兰 (Oveis Gharan) 早期关于旅行推销员问题的研究是这种模式的第一个实例，这种模式在他的整个职业生涯中都会反复出现。
He doesn’t hesitate to plunge into the literature on unfamiliar subjects, from probability theory to statistical physics to abstract math like algebraic geometry, and pluck out new tools to use in his own work.
他毫不犹豫地投入到不熟悉学科的文献中，从概率论到统计物理学，再到代数几何等抽象数学，并找出新工具在自己的工作中使用。
This is what a lot of the brilliant, great researchers do.
This is what a lot of the brilliant, great researchers do.
They connect things that are seemingly disconnected.
它们将看似互不相关的事物联系起来。
“He always liked to read a million papers,” Ronaghi said.
“He always liked to read a million papers,” Ronaghi said.
“He has an infinite amount of capacity for learning new concepts.”
“He has an infinite amount of capacity for learning new concepts.”
Yet to hear Oveis Gharan tell it, research is often a struggle.
然而，据奥韦斯·加兰 (Oveis Gharan) 所说，研究往往是一场斗争。
“It has a lot of ups and downs, mostly downs,” he said.
“It has a lot of ups and downs, mostly downs,” he said.
“You always think, ‘Can I ever come up with something that doesn’t fail?’” He rarely experiences the eureka moments that abound in popular portrayals of mathematical research.
“你总是想，‘我能想出一些不会失败的东西吗？’”他很少经历数学研究流行描述中常见的顿悟时刻。
Instead, working on a proof feels like building a house one brick at a time.
Instead, working on a proof feels like building a house one brick at a time.
There are many ways to assemble the pieces, and only when the whole thing is nearly complete can you be sure that it’s structurally sound.
There are many ways to assemble the pieces, and only when the whole thing is nearly complete can you be sure that it’s structurally sound.
“You put these bricks on top of each other,” he said.
“You put these bricks on top of each other,” he said.
“You never know if you’re doing it the right way.”
“You never know if you’re doing it the right way.”
Oveis Gharan often finds it helpful to busy himself with another activity while mulling over math problems.
Oveis Gharan often finds it helpful to busy himself with another activity while mulling over math problems.
In graduate school, his preferred pastime was another sort of brick stacking — he played so many games of Tetris at his desk that a professor with a nearby office once asked him when he actually did his work.
在研究生院，他最喜欢的消遣是另一种堆砖——他在办公桌上玩了很多俄罗斯方块游戏，以至于附近办公室的一位教授曾经问他什么时候真正开始工作。
At one point the solution to a problem he’d been wrestling with appeared to him in a dream, but he didn’t have a notebook on hand when he woke up to jot down the idea before it faded.
有一次，他一直在努力解决的一个问题的解决方案出现在他的梦中，但当他醒来时，他手边没有笔记本，无法在这个想法消失之前记下它。
For some time after that, he would concentrate on mathematics as he was falling asleep, in hopes of spurring another nocturnal breakthrough, without success.
此后的一段时间里，他会在睡着时集中精力研究数学，希望能激发另一次夜间突破，但没有成功。
“I would end up waking up with a headache,” he said.
“I would end up waking up with a headache,” he said.
Oveis Gharan says he does some of his best thinking when he’s surrounded by nature.
奥维斯·加兰 (Oveis Gharan) 说，当他被大自然包围时，他会做出一些最好的思考。
In graduate school, Oveis Gharan mostly worked alone, checking in with mentors periodically to exchange ideas.
In graduate school, Oveis Gharan mostly worked alone, checking in with mentors periodically to exchange ideas.
Since then, he’s preferred close collaborations that involve frequent marathon brainstorming sessions.
Since then, he’s preferred close collaborations that involve frequent marathon brainstorming sessions.
In 2013, he struck up what would become a long and fruitful collaboration with Nima Anari , a fellow alumnus of the Iranian Informatics Olympiad team who was a graduate student at the University of California, Berkeley when Oveis Gharan arrived on campus for a postdoctoral fellowship.
2013 年，他与伊朗信息学奥林匹克代表队的校友尼玛·阿纳里 (Nima Anari) 建立了长期且富有成果的合作关系，当 Oveis Gharan 来到加州大学伯克利分校攻读博士后奖学金时，尼玛·阿纳里还是加州大学伯克利分校的研究生。
Together, Oveis Gharan and Anari used polynomial methods to make further progress on the asymmetric traveling salesperson problem and settle a longstanding open question in graph theory.
Oveis Gharan 和 Anari 一起使用多项式方法在非对称旅行商问题上取得了进一步的进展，并解决了图论中长期存在的悬而未决的问题。
They then grew interested in a fundamental question about algorithms that harness randomness.
然后，他们对一个有关利用随机性的算法的基本问题产生了兴趣。
These algorithms assume that you can easily pick a random item from a collection of mathematical objects — a task that statisticians call sampling.
这些算法假设您可以轻松地从数学对象的集合中随机选择一个项目——统计学家称之为抽样的任务。
But how exactly do you get that random sample?
但究竟如何获得随机样本呢？
Sampling problems are common in the real world.
抽样问题在现实世界中很常见。
Card games are a classic example: You want your deck to be in a random order before you deal.
Card games are a classic example: You want your deck to be in a random order before you deal.
When you repeatedly shuffle a deck to randomize it, you’re essentially running a type of sampling algorithm called a Markov chain.
当您反复洗牌以使其随机化时，您实际上是在运行一种称为马尔可夫链的采样算法。
Every Markov chain algorithm starts with one item from a large collection of mathematical objects, such as all the possible ways to order a given deck, or all the possible spanning trees of a given graph.
每个马尔可夫链算法都从大量数学对象中的一项开始，例如排序给定牌组的所有可能方法，或给定图的所有可能的生成树。
Then the algorithm repeatedly tweaks this object by introducing a bit of randomness — in the case of spanning trees, each tweak deletes a random edge and adds another to get a new spanning tree.
然后，算法通过引入一点随机性来重复调整该对象 - 在生成树的情况下，每次调整都会删除一个随机边并添加另一个随机边以获得新的生成树。
Repeat this process until that spanning tree no longer bears any trace of the tree you started with.
重复此过程，直到该生成树不再带有您开始使用的树的任何痕迹。
The output of the last step is your random sample.
最后一步的输出是您的随机样本。
To be confident that the sample is truly random, though, you need to know how many times to repeat the process — or, in other words, how long to run the Markov chain.
不过，为了确信样本是真正随机的，您需要知道重复该过程多少次，或者换句话说，马尔可夫链运行多长时间。
This quantity is called the mixing time, and it depends on the mathematical structure of the sampled objects.
这个量称为混合时间，它取决于采样对象的数学结构。
In 1989, the computer scientists Milena Mihail (who died in April 2026) and Umesh Vazirani made an important conjecture about sampling mathematical objects related to spanning trees called matroid bases — a task that has many applications in computer science and beyond.
1989 年，计算机科学家 Milena Mihail（于 2026 年 4 月去世）和 Umesh Vazirani 提出了一个重要猜想，即对与生成树（称为拟阵基）相关的数学对象进行采样，这项任务在计算机科学及其他领域有许多应用。
They proposed that a simple Markov chain could accomplish this sampling task, but they didn’t know how to establish that the Markov chain would have a short enough mixing time.
他们提出一个简单的马尔可夫链可以完成这个采样任务，但他们不知道如何确定马尔可夫链具有足够短的混合时间。
For years, many researchers tried and failed to prove their conjecture.
多年来，许多研究人员尝试证明他们的猜想，但均以失败告终。
“Every technique people had tried before just didn’t get us there,” said Daniel Spielman , a computer scientist at Yale University who wrestled with the problem himself in the 1990s.
耶鲁大学计算机科学家丹尼尔·斯皮尔曼（Daniel Spielman）在 20 世纪 90 年代亲自致力于解决这个问题，他说：“人们之前尝试过的每一种技术都无法让我们实现这一目标。”
“We needed some new math.”
“我们需要一些新的数学。”
Oveis Gharan and Anari teamed up with new collaborators and supplied that new math in 2018.
Oveis Gharan 和 Anari 与新合作者合作，在 2018 年提供了新的数学结果。
Working with the mathematician Cynthia Vinzant , they translated the matroid basis sampling problem into the language of polynomials, just as Oveis Gharan had done when working on the traveling salesperson problem, and identified the key feature shared by those polynomials.
他们与数学家 Cynthia Vinzant 合作，将拟阵基抽样问题翻译成多项式语言，就像 Oveis Gharan 在解决旅行推销员问题时所做的那样，并确定了这些多项式共有的关键特征。
The result was an important breakthrough in pure mathematics in its own right, and it provided them with a useful new tool.
结果本身就是纯数学的一个重要突破，并为他们提供了一个有用的新工具。
Joined by Oveis Gharan’s student Kuikui Liu , the team then used this key feature with other seemingly unrelated tools to finally prove the matroid basis sampling conjecture , 30 years after it was first proposed.
在 Oveis Gharan 的学生 Kuikui Liu 的加入下，该团队将这一关键特征与其他看似无关的工具结合使用，最终在拟阵基采样猜想首次提出 30 年后证明了这一猜想。
“It was a stunning result,” Vazirani said.
“这是一个令人震惊的结果，”瓦齐拉尼说。
“It really did seem like a piece of magic.”
“这确实看起来像是一件魔法。”
Oveis Gharan (right) in 2005, with his siblings (from left) Shahab, Shahram, Sheida, and Shadi.
2005 年，奥韦斯·加兰（Oveis Gharan）（右）和他的兄弟姐妹（左起）Shahab、Shahram、Sheida 和 Shadi。
Courtesy of Shayan Oveis Gharan
由 Shayan Oveis Gharan 提供
The team’s landmark proof sparked a revolution in the study of sampling algorithms.
该团队具有里程碑意义的证明引发了采样算法研究的一场革命。
Oveis Gharan, Anari, and Liu later developed a more general framework for identifying cases where Markov chains mix rapidly, among them mathematical models of materials that have long interested physicists.
Oveis Gharan、Anari 和 Liu 后来开发了一个更通用的框架，用于识别马尔可夫链快速混合的情况，其中包括长期以来引起物理学家兴趣的材料数学模型。
“After that, it felt like everyone and their adviser jumped into the pool,” Spielman said.
“在那之后，感觉每个人和他们的顾问都跳进了泳池，”斯皮尔曼说。
“It’s really changed how the field works.”
“这确实改变了该领域的运作方式。”
In late 2018, as the sampling revolution was just beginning, Oveis Gharan was already itching for another challenge.
2018 年底，采样革命刚刚开始，Oveis Gharan 已经渴望迎接另一次挑战。
He decided it was time to return to the traveling salesperson problem, where his intellectual journey had started a decade earlier.
他决定是时候回到旅行推销员问题了，他的智力之旅十年前就开始了。
He’d picked up many mathematical tools on his travels in the intervening years.
在接下来的几年里，他在旅行中学到了许多数学工具。
Now, he hoped to use those tools to prove that the algorithm he’d helped design as a graduate student would beat Christofides’ algorithm for the most general version of the problem.
现在，他希望利用这些工具来证明他作为研究生时帮助设计的算法能够在解决该问题的最通用版本上击败 Christofides 的算法。
“There’s a certain amount of fearlessness there, to say, ‘I’m going to take this on where everybody else has failed,’” said David Williamson , a veteran traveling salesperson researcher at Cornell University.
康奈尔大学资深旅行推销员研究员戴维·威廉姆森 (David Williamson) 表示：“人们有一定程度的无所畏惧，可以说‘我要在其他人都失败的地方承担起这件事’。”
A decade after it first captured his interest, Oveis Gharan returned to the traveling salesperson problem in late 2018.
在首次引起他的兴趣十年后，Oveis Gharan 于 2018 年底再次关注旅行推销员问题。
Oveis Gharan began working on the problem with Karlin and a new graduate student, Nathan Klein .
奥韦斯·加兰 (Oveis Gharan) 开始与卡林 (Karlin) 和新研究生内森·克莱因 (Nathan Klein) 一起研究这个问题。
They devised new techniques for handling tricky graphs with a lot of overlap between regions that the algorithm needed to analyze separately.
他们设计了新技术来处理棘手的图形，这些图形在算法需要单独分析的区域之间存在大量重叠。
Combining those techniques with Oveis Gharan’s polynomial methods, they resolved another important special case in the spring of 2019 and finally conquered the most general version of the problem in December of that year — breaking the record that Christofides’ algorithm had held for over 40 years.
将这些技术与 Oveis Gharan 的多项式方法相结合，他们在 2019 年春天解决了另一个重要的特例，并最终于当年 12 月攻克了该问题的最普遍版本——打破了 Christofides 算法保持了 40 多年的记录。
It took them another seven months to double-check every detail of the proof and write up the dense 90-page paper describing their result.
他们又花了 7 个月的时间仔细检查证明的每个细节，并写出 90 页厚的论文来描述他们的结果。
Saberi, who’d first introduced Oveis Gharan to the traveling salesperson problem, was stunned by his former student’s achievement.
萨贝里是第一个向奥韦斯·加兰介绍旅行推销员问题的人，他对他以前的学生的成就感到震惊。
“For me, it was like the Wright brothers” cobbling together a primitive plane, he said, “then seeing something akin to a Boeing-747 10 years later.”
“对我来说，这就像莱特兄弟”拼凑了一架原始飞机，“然后在 10 年后看到了类似于波音 747 的飞机。”
Since landing at the University of Washington in 2015, Oveis Gharan has settled into life in Seattle with Ronaghi, who works as the chief technology officer of a start-up she founded as a graduate student.
自 2015 年登陆华盛顿大学以来，Oveis Gharan 与 Ronaghi 一起定居在西雅图，后者在她研究生时创办的一家初创公司担任首席技术官。
He keeps notebooks stashed throughout their house, in case inspiration strikes at odd hours, but he’s grown better at setting work aside, especially when spending time with their 10-year-old son Faraz.
他把笔记本藏在家里各处，以防在闲暇时突发灵感，但他越来越擅长把工作放在一边，尤其是在与 10 岁的儿子法拉兹共度时光时。
“Shayan has an impressive, impressive ability just to play,” Ronaghi said.
“沙扬的比赛能力令人印象深刻，”罗纳吉说。
“His brain can have fun, like a little kid, and not take it too seriously.”
“他的大脑可以像小孩子一样享受乐趣，而不会太认真。”
Even when Oveis Gharan isn’t working, though, the competitive spirit that animated his childhood sometimes comes through.
不过，即使奥韦斯·加兰 (Oveis Gharan) 不工作时，他童年时期的竞争精神有时也会显现出来。
When the Covid-19 pandemic hit, he discovered a passion for cooking, and he approaches that hobby with the same perfectionist attitude that he brings to the rest of his work, especially when he’s hosting.
当 Covid-19 大流行来袭时，他发现了对烹饪的热情，并以与他在其他工作中（尤其是在主持时）同样的完美主义态度来对待这一爱好。
“My kids believe that he’s the best cook in the world,” his sister Shadi said.
“我的孩子们相信他是世界上最好的厨师，”他的妹妹沙迪说。
“I’m like, ‘Dude, relax, you don’t have to be the best in everything.’”
“我说，‘伙计，放松点，你不必在所有事情上都是最好的。’”
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