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This Week’s Citation Classic c~~833~ 1 Taijan R. Depth-first search and linear graph . SIAM!. Comput. 1:146-60, 1972. I [Department of Computer Science, . Ithaca, NY]

The fundamental properties of depth-first search, for a number of graph problems, in2- search as a tool for building efficient graph cluding finding triconnected3 components algorithms are presented and illustrated by and testing graph planarity. The means of two linear-time algorithms, for for the latter4problem became the main part finding the biconnected components of an of my thesis. undirected graph and for finding the strong “I wrote ‘Depth-first search and linear components of a directed graph. [The SC!a graph algorithms’ with two purposes: to ex- indicates that this paper has been cited in plain the theoretical properties of depth- over 105 publications since 1972, making it first search, and to illustrate how those the most-cited paper published in this jour- properties could be used to devise efficient nal to date.] algorithms for problems on both undirected and directed graphs. As an example of the use of depth-first search on undirected graphs, I used a refined version of John’s original biconnected components algo- rithm,5which we also discussed in another Robert E. Tarjan paper. As an example of the use of depth- Bell Laboratories first search on directed graphs, I devised an Murray Hill, NJ 07974 algorithm for finding the strongly connected components of a directed graph. The paper appeared originally6 in the proceedings of a May 12, 1983 conference. “I had some difficulty in getting the strong components algorithm to work cor- “In the summer of 1970, just after my first rectly; my initial attempts had subtle bugs. year as a graduate student at Stanford Uni- Although the algorithm is simple to state versity, John Hopcroft arrived on sabbatical and program and very efficient in practice, from Cornell University. There ensued a proving that it is correct is not easy (and is I very fruitful collaboration. We began work an interesting exercise for program verifiers, almost immediately on efficient graph algo- both human and mechanical), because the rithms. John was interested in finding prob- algorithm interleaves several calculations lems for which one could prove nonlinear that must all proceed simultaneously for the lower bounds on computation time. I sug- method to work. gested the problem of computing the bicon- “I think the paper has been cited so often nected components of a graph as a good because the algorithms it presents are sim- candidate for a problem taking nonlinear ple and widely useful, and because it lays time, but John was able to devise a linear- out the properties of depth-first search on time algorithm for this problem. The main which all depth-first search algorithms de- technique used in the algorithm is depth- pend. Our other depth-first search algo- first search. Depth-first1 search was proposed rithms are both more complicated and more long ago by Trémaux as a maze-searching specialized than the ones presented in the method, but its theoretical properties had paper, and thus are less widely cited. The not been fully exploited at the time we substance of the paper appears in many al- began our work. We were able to obtain gorithms texts, of which the seminal one is 7 linear-time algorithms, based on depth-first by Aho, Hopcroft, and Ullman.”

1. Lucia E. Rgcrjations mathimatiques. Paris: Gauthier-Villars, 1883. Vol. I. 2. Hoperoft SE & Tartan RE. Dividing a graph into triconnecled components. SIAMI. Comput. 2:135-58. 1973. 3. — . Efficient planarity testing. I. Assn. Comput. Mach. 21:549-68, 1974. 4. Tit~auR E. An efficient plonarity algorithm. Stanford, CA: , Computer Science Department, 1971, Technical Report STAN-CS-244-71. 5. Hopcroh 3 E & Turfan R E. Algorithm 447: efficient algorithms for graph manipulation. Commun. ACM 16:372-8, I 973. 6. TurJan R E Depth-first ucarch and linear graph algonthms. Conference record of Twelfth Annual IEEE Symposium on Switching and , 13-15 October 1971. New York: IEEE. 1971. p. 114-21. 7. Abo A V. Hopcroft I E & UIIman I D. The design and analysis of computer algorithms. Reading. MA: Addison-Wesley, 1974. 470 p. 20 ET&AS CURRENT CONTENTS® @1983 by SI® L