Technology Category
Search and Optimization: Heuristic SearchConstraint Satisfaction and Optimization: Distributed CSP/OptimizationKnowledge Representation and Reasoning: Computational Complexity of Reasoning
Fully Dynamic Maintenance of Loop Nesting Forests in Reducible Flow Graphs
🤖 AI Summary
This work addresses the problem of dynamically maintaining loop nesting forests in reducible control flow graphs under edge insertions and deletions. It presents the first fully dynamic algorithm that locally updates the depth-first search (DFS) tree upon graph modifications, thereby avoiding costly global recomputation. The approach leverages dynamic DFS maintenance and incremental graph algorithms, supported by formal invariants and a rigorous correctness proof, to efficiently support real-time updates of loop structures and enable rapid derivation of dominance information. By providing a practical dynamic abstraction for compiler optimizations and program analysis, this study significantly enhances the responsiveness of modern compilation pipelines to changes in control flow.
Technology Category
Application Category
📝 Abstract
Loop nesting forests (LNFs) are a fundamental abstraction for reasoning about control-flow structure, enabling applications such as compiler optimizations, program analysis, and dominator computation. While efficient static algorithms for constructing LNFs are well understood, maintaining them under dynamic graph updates has remained largely unexplored due to the lack of efficient dynamic depth-first search (DFS) maintenance.
In this paper, we present the first fully dynamic algorithm for maintaining loop nesting forests in reducible control-flow graphs. Our approach leverages recent advances in dynamic DFS maintenance to incrementally update loop structure under edge insertions and deletions. We show that updates can be confined to local regions of the depth-first spanning tree, avoiding global recomputation.
We provide formal invariants, correctness arguments, and complexity analysis, and demonstrate how the maintained LNF enables efficient derivation of dominance information. Our results establish LNFs as a practical dynamic abstraction for modern compiler and analysis pipelines.
Problem
Research questions and friction points this paper is trying to address.
loop nesting forests
dynamic graph updates
reducible flow graphs
control-flow analysis
dynamic maintenance
Innovation
Methods, ideas, or system contributions that make the work stand out.
loop nesting forests
dynamic graph algorithms
reducible flow graphs
incremental program analysis
dynamic DFS
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