Robert Endre Tarjan
Born (1948-04-30) April 30, 1948 (age 76)
Pomona, California, United States
Alma materCalifornia Institute of Technology (BS)
Stanford University (MS, PhD)
Known forAlgorithms and data structures
AwardsParis Kanellakis Award (1999)
Turing Award (1986)
Nevanlinna Prize (1982)
Scientific career
FieldsComputer science
InstitutionsPrinceton University
New York University
Stanford University
University of California, Berkeley
Cornell University
Microsoft Research
Intertrust Technologies
NEC Research
Bell Labs
ThesisAn Efficient Planarity Algorithm (1972)
Doctoral advisorRobert W. Floyd
Other academic advisorsDonald Knuth
Doctoral students

Robert Endre Tarjan (born April 30, 1948) is an American computer scientist and mathematician. He is the discoverer of several graph theory algorithms, including his strongly connected components 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.

Personal life and education

He was born in Pomona, California. His father, George Tarjan (1912-1991), raised in Hungary,[1] was a child psychiatrist, specializing in mental retardation, and ran a state hospital.[2] Robert Tarjan's younger brother James became a chess grandmaster.[3] As a child, Robert 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.[4]

While he was in high school, Tarjan got a job, where he worked with 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[5] and Donald Knuth,[6] 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.[7]

Tarjan now lives in Princeton, NJ, and Silicon Valley. He is married to Nayla Rizk.[8] He has three daughters: Alice Tarjan, Sophie Zawacki, and Maxine Tarjan.[9]

Computer science career

Tarjan has been teaching at Princeton University since 1985.[7] 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).[10] 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, Tarjan's strongly connected components algorithm, and Tarjan's bridge-finding 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.[11]

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.[12]


Tarjan received the Turing Award jointly with John Hopcroft in 1986. The citation for the award states[10] 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:[13]

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

Some of the other awards for Tarjan include:

Selected publications

Tarjan's papers have been collectively cited over 94,000 times.[20] Among the most cited are:


Tarjan holds at least 18 U.S. patents.[6] These include:


  1. ^ "Jewish Recipients of the ACM A.M. Turing Award".
  2. ^ a b 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.
  3. ^ Melvin, Shabsin (August 1984). "George Tarjan, M.D. one hundred twelfth president, 1983-1984". The American Journal of Psychiatry. 141 (8): 931–934. doi:10.1176/ajp.141.8.931.
  4. ^ "Robert Tarjan: The Art of the Algorithm". Hewlett-Packard. Retrieved 2010-09-05.
  5. ^ "Robert Endre Tarjan". Mathematics Genealogy Project. Retrieved 2008-01-09.
  6. ^ a b Tarjan, Robert Endre (November 15, 2019). "Curriculum Vitae" (PDF). Archived from the original (PDF) on 2019-11-23. Retrieved 2019-11-23.
  7. ^ a b "Robert Endre Tarjan: The art of the algorithm (interview)". Hewlett-Packard. September 2004. Retrieved 2008-01-09.
  8. ^ "Nayla Rizk and Robert Tarjan". The New York Times. July 2013.
  9. ^ "Photos from Bob Tarjan's 60th Birthday Symposium". DIMACS. May 2008.
  10. ^ a b c d e King, V. "Robert E Tarjan — A.M. Turing Award Laureate". ACM. Retrieved 2014-01-19.
  11. ^ 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.
  12. ^ Tarjan, Robert E.; van Leeuwen, Jan (1984). "Worst-case analysis of set union algorithms". Journal of the ACM. 31 (2): 245–281. doi:10.1145/62.2160. S2CID 5363073.
  13. ^ "Fellows Award — Robert E. Tarjan". ACM. September 25, 1998. Retrieved 2005-11-18.
  14. ^ "Rolf Nevanlinna Prize Winners". International Mathematical Union. Archived from the original on 2008-12-27. Retrieved 2014-01-19.
  15. ^ "Robert Endre Tarjan". American Academy of Arts & Sciences. Retrieved 2020-06-15.
  16. ^ "Robert Tarjan". Retrieved 2020-06-15.
  17. ^ "Dr. Robert E. Tarjan". NAE Website. Retrieved 2020-06-15.
  18. ^ "APS Member History". Retrieved 2022-04-19.
  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.
  20. ^ "Robert Tarjan Google Scholar Page". Google Scholar. Retrieved 6 March 2023.
  21. ^ Tarjan, Robert (1972-06-01). "Depth-First Search and Linear Graph Algorithms". SIAM Journal on Computing. 1 (2): 146–160. doi:10.1137/0201010. ISSN 0097-5397. S2CID 16467262.
  22. ^ Fredman, Michael L.; Tarjan, Robert Endre (1987-07-01). "Fibonacci heaps and their uses in improved network optimization algorithms". Journal of the ACM. 34 (3): 596–615. doi:10.1145/28869.28874. ISSN 0004-5411. S2CID 7904683.
  23. ^ "Back Matter". Data Structures and Network Algorithms: 125–131. January 1983. doi:10.1137/ ISBN 978-0-89871-187-5.
  24. ^ Goldberg, Andrew V.; Tarjan, Robert E. (1988-10-01). "A new approach to the maximum-flow problem". Journal of the ACM. 35 (4): 921–940. doi:10.1145/48014.61051. ISSN 0004-5411. S2CID 14492800.
  25. ^ Bentley, Jon L.; Sleator, Daniel D. K.; Tarjan, Robert E. (January 3, 1989). "United States Patent 4796003 — Data compaction".
  26. ^ 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".
  27. ^ 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".