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
Bob Tarjan.jpg
Born (1948-04-30) April 30, 1948 (age 74)
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

Early life and educationEdit

He was born in Pomona, California. His father, raised in Hungary,[2] was a child psychiatrist, specializing in mental retardation, and ran a state hospital.[3] 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.[4]

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.[3]

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]

Computer science careerEdit

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).[8] 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 structuresEdit

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.[9]

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.[10]


Tarjan received the Turing Award jointly with John Hopcroft in 1986. The citation for the award states[8] 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:[11]

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

Some of the other awards for Tarjan include:


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

  • J. Bentley, D. Sleator, and R. E. Tarjan, U. S. Patent 4,796,003, Data Compaction, 1989[18]
  • 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[19]
  • B. Pinkas, S. Haber, R. E. Tarjan, and T. Sander, U. S. Patent 8220036, Establishing a secure channel with a human user, 2012[20]

Research papersEdit

According to Google Scholar he has published over 500 research papers which have been cited over 80,000 times.[21]

Some of his top papers include:

  • 1972: Depth-first search and linear graph algorithms, R Tarjan, SIAM Journal on Computing 1 (2), 146-160[22]
  • 1987: Fibonacci heaps and their uses in improved network optimization algorithms, ML Fredman, RE Tarjan, Journal of the ACM (JACM) 34 (3), 596-615[23]
  • 1983: Data structures and network algorithms, RE Tarjan, Society for industrial and Applied Mathematics[24]
  • 1988: A new approach to the maximum-flow problem, V Goldberg, RE Tarjan, Journal of the ACM (JACM) 35 (4), 921-940[25]


  1. ^ "Intertrust Leadership".
  2. ^ "Jewish Recipients of the ACM A.M. Turing Award".
  3. ^ 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.
  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. ^ a b c d e King, V. "Robert E Tarjan — A.M. Turing Award Laureate". ACM. Retrieved 2014-01-19.
  9. ^ 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.
  10. ^ 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.
  11. ^ "Fellows Award — Robert E. Tarjan". ACM. September 25, 1998. Retrieved 2005-11-18.
  12. ^ "Rolf Nevanlinna Prize Winners". International Mathematical Union. Archived from the original on 2008-12-27. Retrieved 2014-01-19.
  13. ^ "Robert Endre Tarjan". American Academy of Arts & Sciences. Retrieved 2020-06-15.
  14. ^ "Robert Tarjan". Retrieved 2020-06-15.
  15. ^ "Dr. Robert E. Tarjan". NAE Website. Retrieved 2020-06-15.
  16. ^ "APS Member History". Retrieved 2022-04-19.
  17. ^ "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.
  18. ^ Bentley, Jon L.; Sleator, Daniel D. K.; Tarjan, Robert E. (January 3, 1989). "United States Patent 4796003 — Data compaction".
  19. ^ 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".
  20. ^ 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".
  21. ^ "Robert Tarjan". Retrieved 2021-02-02.
  22. ^ 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.
  23. ^ 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.
  24. ^ "Back Matter". Data Structures and Network Algorithms: 125–131. January 1983. doi:10.1137/ ISBN 978-0-89871-187-5.
  25. ^ 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.


  • 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  

External linksEdit

  • Robert E. Tarjan at DBLP Bibliography Server  
  • List of Robert Tarjan's patents on IPEXL's Patent Directory
  • Robert Tarjan's home page at Princeton.
  • Robert Endre Tarjan at the Mathematics Genealogy Project  
  • "Robert Tarjan: Search Tree Mysteries". YouTube. princetonacademics. August 24, 2012.
  • "Robert E. Tarjan lecture at the University of Latvia: Zip Trees". YouTube. Lativjas Universitäte. September 4, 2018.
  • "Robert E. Tarjan, Concurrent Connected Components, University of Vienna, Communication Technologies". YouTube. Peter Kindermann. February 20, 2019.
  • "Robert E Tarjan, 1986 ACM Turing Award Recipient". YouTube. Association for Computing Machiners (ACM). June 11, 2019. (interview by Roy Levin, July 12, 2017)
  • "7th HLF – Lecture: Robert Endre Tarjan". YouTube. Heidelberg Laureate Forum. September 24, 2019.