Optimization of array accesses by collective loop transformations
ICS '91 Proceedings of the 5th international conference on Supercomputing
A data locality optimizing algorithm
PLDI '91 Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation
The complexity of multiway cuts (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The high performance Fortran handbook
The high performance Fortran handbook
Optimal weighted loop fusion for parallel programs
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
The implementation and evaluation of fusion and contraction in array languages
PLDI '98 Proceedings of the ACM SIGPLAN 1998 conference on Programming language design and implementation
Loop parallelization algorithms: from parallelism extraction to code generation
Parallel Computing - Special issues on languages and compilers for parallel computers
Tools and techniques for automatic data layout: a case study
Parallel Computing - Special issues on languages and compilers for parallel computers
Automatic storage management for parallel programs
Parallel Computing - Special issues on languages and compilers for parallel computers
A Linear Algebra Framework for Automatic Determination of Optimal Data Layouts
IEEE Transactions on Parallel and Distributed Systems
On the complexity of loop fusion
Parallel Computing - Special issue on new trends on scheduling in parallel and distributed systems
Data locality enhancement by memory reduction
ICS '01 Proceedings of the 15th international conference on Supercomputing
Blocking and array contraction across arbitrarily nested loops using affine partitioning
PPoPP '01 Proceedings of the eighth ACM SIGPLAN symposium on Principles and practices of parallel programming
Optimizing Supercompilers for Supercomputers
Optimizing Supercompilers for Supercomputers
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Precise Data Locality Optimization of Nested Loops
The Journal of Supercomputing
Collective Loop Fusion for Array Contraction
Proceedings of the 5th International Workshop on Languages and Compilers for Parallel Computing
Maximizing Loop Parallelism and Improving Data Locality via Loop Fusion and Distribution
Proceedings of the 6th International Workshop on Languages and Compilers for Parallel Computing
Complexity of Multi-dimensional Loop Alignment
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
High-Level Synthesis of Nonprogrammable Hardware Accelerators
ASAP '00 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Integrating Loop and Data Transformations for Global Optimisation
PACT '98 Proceedings of the 1998 International Conference on Parallel Architectures and Compilation Techniques
Proceedings of the 2007 ACM SIGPLAN/SIGBED conference on Languages, compilers, and tools for embedded systems
Improved loop tiling based on the removal of spurious false dependences
ACM Transactions on Architecture and Code Optimization (TACO) - Special Issue on High-Performance Embedded Architectures and Compilers
| Hi-index | 0.00 |
Array contraction is an optimization that transforms array variables into scalar variables within a loop. While the opposite transformation, scalar expansion, is used for enabling parallelism (with a penalty in memory size), array contraction is used to save memory by removing temporary arrays and to increase locality. Several heuristics have already been proposed to perform array contraction through loop fusion and/or loop shifting. But until now, the complexity of the problem was unknown, and no exact approach was available (and even more, only a sufficient condition for array contraction was used). In this paper, we focus on the theoretical aspects of the problem. We prove several NP-complete results that characterize precisely its complexity and we provide an integer linear programming formulation to solve the problem exactly. Our study also proves the NP-completeness of similar problems whose complexity was not established so far.