A Labeling Approach to Incremental Cycle Detection

In the incremental cycle detection problem arcs are added to a directed acyclic graph and the algorithm has to report if the new arc closes a cycle. One seeks to minimize the total time to process the entire sequence of arc insertions, or until a cycle appears. In a recent breakthrough, Bender, Fineman, Gilbert and Tarjan [6] presented two different algorithms, with time complexity O(n log n) and O(m ·min{m, n}), respectively. In this paper we introduce a new technique for incremental cycle detection that allows us to obtain both bounds (up to a logarithmic factor). Furthermore, our approach seems more amiable for distributed implementation. ∗Microsoft Research – SVC, USA. [email protected] †Tel Aviv University, Tel Aviv, Israel. {fiat,haimk}@cs.tau.ac.il ‡Bar Ilan University, Ramat Gan, Israel. [email protected] ar X iv :1 31 0. 83 81 v1 [ cs .D S] 3 1 O ct 2 01 3