	Title:Steiner Trees
	Name: Ronald Graham University of California, San Diego
	Time:October 13th (Monday) 09:00-09:45
	Location: Lecture Hall, FIT Building, Tsinghua University
	Host Unit: ITCS, Tsinghua University

Abstract

Given a finite set X of points in some metric space M, a fundamental problem in computational geometry involves the construction of the minimum spanning tree MST (X) for X, that is, the tree interconnecting all the points of X having the least possible total length. As is well known, there are a number of efficient algorithms for finding an MST (X). A much more challenging variant asks for the minimum possible length of MST (Y) over all possible supersets Y ? X. Such trees are usually called minimum Steiner trees for X, and have been studied for over 170 years since they were first introduced in 1836. In this talk I will give an overview of what we currently know about these minimum Steiner trees, as well as describing many things that are still unknown.

Biography

Ronald Lewis Graham (born October 31, 1935) is a mathematician credited by the American Mathematical Society with being "one of the principal architects of the rapid development worldwide of discrete Mathematics in recent years". He has done important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness.
He holds the posts of Chief Scientist at the California Institute for Telecommunication and Information Technology (also known as Cal-(IT)2), and Irwin and Joan Jacobs Professor at the Department of Computer Science and Engineering of the University of California, San Diego (UCSD).
He was born in Taft, California. In 1962, he got his Ph.D. in Mathematics from the University of California, Berkeley.

A 1977 paper of his discussed a problem in Ramsey theory, and gave a large number as an upper bound for its solution. This number has since become famous as the largest number ever used in a serious mathematical proof (and is listed in the Guinness Book of Records as such), and is now known as Graham's number.

Graham popularized the concept of the Erd?s number, named after the highly prolific Hungarian mathematician Paul Erd?s (1913 - 1996). A mathematician's Erd?s number is the minimum number of links away from Erd?s they are, where mathematician A is linked to mathematician B if they have co-authored a paper. Graham's Erd?s number is 1. He co-authored nearly 30 papers with Erd?s, and was also a good friend. Erd?s often stayed with him, and let him look after his mathematical papers and even his money for him. Between 1993 and 1994 Graham served as the president of the American Mathematical Society. Graham was also featured in Ripley's Believe It or Not for being not only "one of the world's foremost mathematicians", but also "a highly skilled trampolinist and juggler", and past president of the International Jugglers' Association. In 2003, Graham won the American Mathematical Society's annual Steele Prize for Lifetime Achievement. The prize was awarded on January 16 that year, at the Joint Mathematics Meetings in Baltimore, Maryland. In 1999 he was inducted as a Fellow of the Association for Computing Machinery. Graham, prolific mathematician and industrious human being, has won many other prizes over the years; he was one of the laureates of the prestigious P��lya Prize the first year it was ever awarded, and among the first to win the Euler Medal. The Mathematical Association of America has also awarded him both the Lester R. Ford prize which was "...established in 1964 to recognize authors of articles of expository excellence published in The American Mathematical Monthly...", and the Carl Allendoerfer prize which was established in 1976 for the same reasons, however for a different magazine, the Mathematics Magazine.

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