Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
Elimination algorithms for data flow analysis
ACM Computing Surveys (CSUR)
Algorithm design: a recursion transformation framework
Algorithm design: a recursion transformation framework
On an asymptotic method in enumeration
Journal of Combinatorial Theory Series A
Average-case analysis of algorithms and data structures
Handbook of theoretical computer science (vol. A)
Efficiently computing static single assignment form and the control dependence graph
ACM Transactions on Programming Languages and Systems (TOPLAS)
Efficient program analysis using DJ graphs
Efficient program analysis using DJ graphs
A new framework for elimination-based data flow analysis using DJ graphs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
SIAM Journal on Computing
The Java Programming Language
On loops, dominators, and dominance frontiers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Concrete Math
Data-Flow Frameworks for Worst-Case Execution Time Analysis
Real-Time Systems
Finding dominators revisited: extended abstract
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Programming in Modula-2
Modeling complex flows for worst-case execution time analysis
RTSS'10 Proceedings of the 21st IEEE conference on Real-time systems symposium
Efficient liveness computation using merge sets and DJ-graphs
ACM Transactions on Architecture and Code Optimization (TACO) - HIPEAC Papers
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Sreedhar et al. [V.C. Sreedhar, G.R. Gao, Y.-F. Lee, A new framework for elimination-based data flow analysis using DJ graphs, ACM Trans. Program. Lang. Syst. 20 (2) (1998) 388-435; V.C. Sreedhar, Efficient program analysis using DJ graphs, PhD thesis, School of Computer Science, McGill University, Montreal, Quebec, Canada, 1995] have presented an elimination-based algorithm to solve data flow problems. A thorough analysis of the algorithm shows that the worst-case performance is at least quadratic in the number of nodes of the underlying graph. In contrast, Sreedhar reports a linear time behavior based on some practical applications. In this paper we prove that for goto-free programs, the average case behavior is indeed linear. As a byproduct our result also applies to the average size of the so-called dominance frontier. A thorough average case analysis based on a graph grammar is performed by studying properties of the j-edges in DJ graphs. It appears that this is the first time that a graph grammar is used in order to analyze an algorithm. The average linear time of the algorithm is obtained by classic techniques in the analysis of algorithms and data structures such as singularity analysis of generating functions and transfer lemmas.