Computational geometry: an introduction
Computational geometry: an introduction
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
Multidimensional divide-and-conquer
Communications of the ACM
Proceedings of the 17th International Conference on Data Engineering
Quality adaptation in a multisession multimedia system: model, algorithms, and architecture
Quality adaptation in a multisession multimedia system: model, algorithms, and architecture
Algorithms to identify pareto points in multi-dimensional data sets
Algorithms to identify pareto points in multi-dimensional data sets
ACSD '05 Proceedings of the Fifth International Conference on Application of Concurrency to System Design
Maximal vector computation in large data sets
VLDB '05 Proceedings of the 31st international conference on Very large data bases
A Reactive Local Search-Based Algorithm for the Multiple-Choice Multi-Dimensional Knapsack Problem
Computational Optimization and Applications
Solving the multidimensional multiple-choice knapsack problem by constructing convex hulls
Computers and Operations Research
A calculator for Pareto points
Proceedings of the conference on Design, automation and test in Europe
Fundamenta Informaticae - The Fourth Special Issue on Applications of Concurrency to System Design (ACSD05)
NTHU-Route 2.0: a fast and stable global router
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
FastRoute 4.0: global router with efficient via minimization
Proceedings of the 2009 Asia and South Pacific Design Automation Conference
Proceedings of the 46th Annual Design Automation Conference
Iterative Relaxation-Based Heuristics for the Multiple-choice Multidimensional Knapsack Problem
HM '09 Proceedings of the 6th International Workshop on Hybrid Metaheuristics
Completing high-quality global routes
Proceedings of the 19th international symposium on Physical design
A column generation method for the multiple-choice multi-dimensional knapsack problem
Computational Optimization and Applications
A pareto-algebraic framework for signal power optimization in global routing
Proceedings of the 16th ACM/IEEE international symposium on Low power electronics and design
Fast multidimension multichoice knapsack heuristic for MP-SoC runtime management
ACM Transactions on Embedded Computing Systems (TECS)
Computers and Operations Research
MGR: multi-level global router
Proceedings of the International Conference on Computer-Aided Design
A New Heuristic for Solving the Multichoice Multidimensional Knapsack Problem
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Many combinatorial optimization problems in the embedded systems and design automation domains involve decision making in multidimensional spaces. The multidimensional multiple-choice knapsack problem (MMKP) is among the most challenging of the encountered optimization problems. MMKP problem instances appear for example in chip multiprocessor runtime resource management and in global routing of wiring in circuits. Chip multiprocessor resource management requires solving MMKP under real-time constraints, whereas global routing requires scalability of the solution approach to extremely large MMKP instances. This article presents a novel MMKP heuristic, CPH (for Compositional Pareto-algebraic Heuristic), which is a parameterized compositional heuristic based on the principles of Pareto algebra. Compositionality allows incremental computation of solutions. The parameterization allows tuning of the heuristic to the problem at hand. These aspects make CPH a very versatile heuristic. When tuning CPH for computation time, MMKP instances can be solved in real time with better results than the fastest MMKP heuristic so far. When tuning CPH for solution quality, it finds several new solutions for standard benchmarks that are not found by any existing heuristic. CPH furthermore scales to extremely large problem instances. We illustrate and evaluate the use of CPH in both chip multiprocessor resource management and in global routing.