A Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

A preliminary version of this article appeared in Proceedings of the 35th International Colloquium on Automata, Languages, and Programming (ICALP), Reykjavik, Iceland, July 7-11, 2008. Author’s addresses: Bernhard Haeupler, CSAIL, Massachusetts Institute of Technology, Cambridge, MA 02139, United States, [email protected]; work done while the author was a visiting student at Princeton University). Telikepalli Kavitha, Tata Institute of Fundamental Research, Mumbai, India, [email protected]. Rogers Mathew, Indian Institute of Science, Bangalore, India, [email protected]. Siddhartha Sen, Department of Computer Science, Princeton University, Princeton, NJ 08540, United States, [email protected]. Robert E. Tarjan, Department of Computer Science, Princeton University, Princeton, NJ 08540, United States and HP Laboratories, Palo Alto, CA 94304, United States, [email protected]. Research at Princeton University partially supported by NSF grants CCF-0830676 and CCF-0832797. The information contained herein does not necessarily reflect the opinion or policy of the federal government and no official endorsement should be inferred. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or [email protected]. c © YYYY ACM 1549-6325/YYYY/01-ARTA $10.00 DOI 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000