# Robert Tarjan

**Robert Endre Tarjan** (born April 30, 1948) is an American computer scientist and mathematician. He is the discoverer of several graph algorithms, including Tarjan's off-line lowest common ancestors algorithm, and co-inventor of both splay trees and Fibonacci heaps. Tarjan is currently the James S. McDonnell Distinguished University Professor of Computer Science at Princeton University, and the Chief Scientist at Intertrust Technologies Corporation.[1]

Robert Endre Tarjan | |
---|---|

Born | |

Citizenship | American |

Alma mater | California Institute of Technology (BS) Stanford University (MS, PhD) |

Known for | Algorithms and data structures |

Awards | Paris Kanellakis Award (1999) Turing Award (1986) Nevanlinna Prize (1982) |

Scientific career | |

Fields | Computer science |

Institutions | Princeton University New York University Stanford University University of California, Berkeley Cornell University Microsoft Research Intertrust Technologies Hewlett-Packard Compaq NEC Research Bell Labs |

Thesis | An Efficient Planarity Algorithm (1972) |

Doctoral advisor | Robert W. Floyd |

Other academic advisors | Donald Knuth |

Website | www |

## Early life and education

He was born in Pomona, California. His father was a child psychiatrist specializing in mental retardation, and ran a state hospital.[2] As a child, Tarjan read a lot of science fiction, and wanted to be an astronomer. He became interested in mathematics after reading Martin Gardner's mathematical games column in Scientific American. He became seriously interested in math in the eighth grade, thanks to a "very stimulating" teacher.[3]

While he was in high school, Tarjan got a job, where he worked IBM punch card collators. He first worked with real computers while studying astronomy at the Summer Science Program in 1964.[2]

Tarjan obtained a Bachelor's degree in mathematics from the California Institute of Technology in 1969. At Stanford University, he received his master's degree in computer science in 1971 and a Ph.D. in computer science (with a minor in mathematics) in 1972. At Stanford, he was supervised by Robert Floyd[4] and Donald Knuth,[5] both highly prominent computer scientists, and his Ph.D. dissertation was *An Efficient Planarity Algorithm*. Tarjan selected computer science as his area of interest because he believed that computer science was a way of doing mathematics that could have a practical impact.[6]

## Computer science career

Tarjan has been teaching at Princeton University since 1985.[6] He has also held academic positions at Cornell University (1972–73), University of California, Berkeley (1973–1975), Stanford University (1974–1980), and New York University (1981–1985). He has also been a fellow of the NEC Research Institute (1989–1997).[7] In April 2013 he joined Microsoft Research Silicon Valley in addition to the position at Princeton. In October 2014 he rejoined Intertrust Technologies as chief scientist.

Tarjan has worked at AT&T Bell Labs (1980–1989), Intertrust Technologies (1997–2001, 2014–present), Compaq (2002) and Hewlett Packard (2006–2013).

### Algorithms and data structures

Tarjan is known for his pioneering work on graph theory algorithms and data structures. Some of his well-known algorithms include Tarjan's off-line least common ancestors algorithm, and Tarjan's strongly connected components algorithm, and he was one of five co-authors of the median of medians linear time selection algorithm. The Hopcroft–Tarjan planarity testing algorithm was the first linear-time algorithm for planarity-testing.[8]

Tarjan has also developed important data structures such as the Fibonacci heap (a heap data structure consisting of a forest of trees), and the splay tree (a self-adjusting binary search tree; co-invented by Tarjan and Daniel Sleator). Another significant contribution was the analysis of the disjoint-set data structure; he was the first to prove the optimal runtime involving the inverse Ackermann function.

## Awards

Tarjan received the Turing Award jointly with John Hopcroft in 1986. The citation for the award states[7] that it was:

For fundamental achievements in the design and analysis of algorithms and data structures.

Tarjan was also elected an ACM Fellow in 1994. The citation for this award states:[9]

For seminal advances in the design and analysis of data structures and algorithms.

Some of the other awards for Tarjan include:

- Nevanlinna Prize in Information Science (1983)[7] – first recipient[10]
- National Academy of Sciences Award for Initiatives in Research (1984)[7]
- Paris Kanellakis Award in Theory and Practice, ACM (1999)[7]
- Blaise Pascal Medal in Mathematics and Computer Science, European Academy of Sciences (2004)[7]
- Caltech Distinguished Alumni Award, California Institute of Technology (2010)[11]

## Patents

Tarjan holds at least 18 U.S. patents.[5] These include:

- J. Bentley, D. Sleator, and R. E. Tarjan, U. S. Patent 4,796,003,
*Data Compaction*, 1989[12] - N. Mishra, R. Schreiber, and R. E. Tarjan, U. S. Patent 7,818,272,
*Method for discovery of clusters of objects in an arbitrary undirected graph using a difference between a fraction of internal connections and maximum fraction of connections by an outside object*, 2010[13] - B. Pinkas, S. Haber, R. E. Tarjan, and T. Sander, U. S. Patent 8220036,
*Establishing a secure channel with a human user*, 2012[14]

## Notes

- "Intertrust Leadership".
*intertrust.com*. - Shasha, Dennis Elliott; Lazere, Cathy A. (1998) [1995]. "Robert E. Tarjan: In Search of Good Structure".
*Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists*. Copernicus/Springer. pp. 102–119. ISBN 978-0-387-97992-2. OCLC 32240355. - "Robert Tarjan: The Art of the Algorithm". Hewlett-Packard. Retrieved 2010-09-05.
- "Robert Endre Tarjan". Mathematics Genealogy Project. Retrieved 2008-01-09.
- Tarjan, Robert Endre (November 15, 2019). "Curriculum Vitae" (PDF). Archived from the original (PDF) on 2019-11-23. Retrieved 2019-11-23.
- "Robert Endre Tarjan: The art of the algorithm (interview)". Hewlett-Packard. September 2004. Retrieved 2008-01-09.
- King, V. "Robert E Tarjan — A.M. Turing Award Laureate". ACM. Retrieved 2014-01-19.
- Kocay, William; Kreher, Donald L (2005). "Planar Graphs".
*Graphs, algorithms, and optimization*. Boca Raton: Chapman & Hall/CRC. p. 312. ISBN 978-1-58488-396-8. OCLC 56319851. - "Fellows Award — Robert E. Tarjan". ACM. September 25, 1998. Retrieved 2005-11-18.
- "Rolf Nevanlinna Prize Winners". International Mathematical Union. Archived from the original on 2008-12-27. Retrieved 2014-01-19.
- "Caltech Names Five Distinguished Alumni" (Press release). California Institute of Technology. 2010-03-15. Archived from the original on 2010-10-10. Retrieved 2010-08-26.
- Bentley, Jon L.; Sleator, Daniel D. K.; Tarjan, Robert E. (January 3, 1989). "United States Patent 4796003 — Data compaction".
- Nina, Mishra; Schreiber, Robert Samuel; Robert E., Tarjan (October 19, 2010). "United States Patent 7818272 — Method for discovery of clusters of objects in an arbitrary undirected graph using a difference between a fraction of internal connections and maximum fraction of connections by an outside object".
- Pinkas, Binyamin; Haber, Stuart A.; Tarjan, Robert E.; Sander, Tomas (July 10, 2012). "United States Patent 8220036 — Establishing a secure channel with a human user".

## References

- Tarjan, Robert E. (1983).
*Data structures and network algorithms*. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-187-5. OCLC 10120539. - Tarjan, Robert E.; Pólya, George; Woods, Donald R. (1983).
*Notes on introductory combinatorics*. Boston: Birkhauser. ISBN 978-0-8176-3170-3. OCLC 10018128. - OCLC entries for Robert E Tarjan
- Robert E. Tarjan at DBLP Bibliography Server