Theory of linear and integer programming
Theory of linear and integer programming
Enumerative combinatorics
Calculus of space-optimal mappings of systolic algorithms on processor arrays
Journal of VLSI Signal Processing Systems - Special issue: application specific array processors
Processor allocation and loop scheduling on multiprocessor computers
ICS '92 Proceedings of the 6th international conference on Supercomputing
A practical data flow framework for array reference analysis and its use in optimizations
PLDI '93 Proceedings of the ACM SIGPLAN 1993 conference on Programming language design and implementation
Array-data flow analysis and its use in array privatization
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Counting solutions to Presburger formulas: how and why
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
ICS '96 Proceedings of the 10th international conference on Supercomputing
Parameterized polyhedra and their vertices
International Journal of Parallel Programming
SIGMETRICS '86/PERFORMANCE '86 Proceedings of the 1986 ACM SIGMETRICS joint international conference on Computer performance modelling, measurement and evaluation
Dependence Analysis for Supercomputing
Dependence Analysis for Supercomputing
Estimation of Nested Loops Execution Time by Integer Arithmetic in Convex Polyhedra
Proceedings of the 8th International Symposium on Parallel Processing
On Estimating and Enhancing Cache Effectiveness
Proceedings of the Fourth International Workshop on Languages and Compilers for Parallel Computing
Symbolic Analysis: A Basis for Parallelization, Optimization, and Scheduling of Programs
Proceedings of the 6th International Workshop on Languages and Compilers for Parallel Computing
Compaan: deriving process networks from Matlab for embedded signal processing architectures
CODES '00 Proceedings of the eighth international workshop on Hardware/software codesign
Energy estimation of nested loop programs
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Precise Data Locality Optimization of Nested Loops
The Journal of Supercomputing
Communication Optimization for Affine Recurrence Equations Using Broadcast and Locality
International Journal of Parallel Programming
Design Space Exploration for Massively Parallel Processor Arrays
PaCT '01 Proceedings of the 6th International Conference on Parallel Computing Technologies
Generation of Distributed Loop Control
Embedded Processor Design Challenges: Systems, Architectures, Modeling, and Simulation - SAMOS
Data Sequence Locality: A Generalization of Temporal Locality
Euro-Par '01 Proceedings of the 7th International Euro-Par Conference Manchester on Parallel Processing
Generation of distributed loop control
Embedded processor design challenges
An introduction to processor-time-optimal systolic arrays
Highly parallel computaions
Translating affine nested-loop programs to process networks
Proceedings of the 2004 international conference on Compilers, architecture, and synthesis for embedded systems
Analytical computation of Ehrhart polynomials: enabling more compiler analyses and optimizations
Proceedings of the 2004 international conference on Compilers, architecture, and synthesis for embedded systems
Solving Out-of-Order Communication in Kahn Process Networks
Journal of VLSI Signal Processing Systems
Generating cache hints for improved program efficiency
Journal of Systems Architecture: the EUROMICRO Journal
Some ways to reduce the space dimension in polyhedra computations
Formal Methods in System Design
SPM Conscious Loop Scheduling for Embedded Chip Multiprocessors
ICPADS '06 Proceedings of the 12th International Conference on Parallel and Distributed Systems - Volume 1
Memory optimization by counting points in integer transformations of parametric polytopes
CASES '06 Proceedings of the 2006 international conference on Compilers, architecture and synthesis for embedded systems
Computation of storage requirements for multi-dimensional signal processing applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Counting with rational generating functions
Journal of Symbolic Computation
Journal of Signal Processing Systems
Guidance of Loop Ordering for Reduced Memory Usage in Signal Processing Applications
Journal of Signal Processing Systems
Trade-offs in loop transformations
ACM Transactions on Design Automation of Electronic Systems (TODAES)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Cartesian factoring of polyhedra in linear relation analysis
SAS'03 Proceedings of the 10th international conference on Static analysis
Symbolic and analytic techniques for resource analysis of java bytecode
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Simulating and optimizing a peer-to-peer computing framework
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
On the Occurrence Probability of Local Binary Patterns: A Theoretical Study
Journal of Mathematical Imaging and Vision
Adaptive runtime selection of parallel schedules in the polytope model
Proceedings of the 19th High Performance Computing Symposia
Polyhedral parallelization of binary code
ACM Transactions on Architecture and Code Optimization (TACO) - HIPEAC Papers
Experiences with enumeration of integer projections of parametric polytopes
CC'05 Proceedings of the 14th international conference on Compiler Construction
Integer affine transformations of parametric ℤ-polytopes and applications to loop nest optimization
ACM Transactions on Architecture and Code Optimization (TACO)
Scan detection and parallelization in "inherently sequential" nested loop programs
Proceedings of the Tenth International Symposium on Code Generation and Optimization
Memory partitioning for multidimensional arrays in high-level synthesis
Proceedings of the 50th Annual Design Automation Conference
Presburger arithmetic, rational generating functions, and quasi-polynomials
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Theory and algorithm for generalized memory partitioning in high-level synthesis
Proceedings of the 2014 ACM/SIGDA international symposium on Field-programmable gate arrays
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In the area of automatic parallelization of programs, analyzing and transforming loop nests with parametric affine loop bounds requires fundamental mathematical results. The most common geometrical model of iteration spaces, called the polytope model, is based on mathematics dealing with convex and discrete geometry, linear programming, combinatorics and geometry of numbers.In this paper, we present automatic methods for computing the parametric vertices and the Ehrhart polynomial, i.e., a parametric expression of the number of integer points, of a polytope defined by a set of parametric linear constraints.These methods have many applications in analysis and transformations of nested loop programs. The paper is illustrated with exact symbolic array dataflow analysis, estimation of execution time, and with the computation of the maximum available parallelism of given loop nests.