Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
A fast algorithm for finding dominators in a flowgraph
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic program analysis in almost linear time
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Symbolic evaluation and the global value graph
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
An &Ohgr;(n2 log n) lower bound to the shortest paths problem
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Reference machines require non-linear time to maintain disjoint sets
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
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We devise a method for computing functions defined on paths in trees. The method is based on tree manipulation techniques first used for efficiently representing equivalence relations. It has an almost-linear running time. We apply the method to give O(m $\alpha$(m,n)) algorithms for two problems. A. Verifying a minimum spanning tree in an undirected graph (best previous bound: O(m log log n) ). B. Finding dominators in a directed graph (best previous bound: O(n log n + m) ). Here n is the number of vertices and m the number of edges in the problem graph, and $\alpha$(m,n) is a very slowly growing function which is related to a functional inverse of Ackermann''s function. The method is also useful for solving, in O(m $\alpha$(m,n)) time, certain kinds of pathfinding problems on reducible graphs. Such problems occur in global flow analysis of computer programs and in other contexts. A companion paper will discuss this application.