Fully Dynamic Cycle-Equivalence in Graphs

Two edges el and e2 of an undirected graph are cycle-equivalent iff all cycles that contain el also contain e2, i.e., iff el and e2 are a cut-edge pair. The cycle-equivalence classes of the control-flow graph are used in optimizing compilers to speed up ezasting control-flow and data-flow algorithms. While the cycle-equivalence classes can be computed in linear time, we present the first fully dynamic algorithm for maintaining the cycle-equivalence relation. In an nnode graph OUT data structure executes an edge insertion OT deletion in O(fi1ogn) time and answers the query whether two given edges are cycle-equivalent in O(log2n) time. W e also present an algorithm for plane graphs with O(1ogn) update and query time and for planar graphs with O(1ogn) insertion time and O(log2 n) que y and deletion time. Additionally, we show a lower bound of R(lognllog1ogn) for the amortized tame per operation for the dynamic cycleequivalence problem in the cell probe model.