Multiple-Way Network Partitioning
IEEE Transactions on Computers
A parallel bottom-up clustering algorithm with applications to circuit partitioning in VLSI design
DAC '93 Proceedings of the 30th international Design Automation Conference
A general framework for vertex orderings, with applications to netlist clustering
ICCAD '94 Proceedings of the 1994 IEEE/ACM international conference on Computer-aided design
Multi-way partitioning via spacefilling curves and dynamic programming
DAC '94 Proceedings of the 31st annual Design Automation Conference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Finding a Maximum Density Subgraph
Finding a Maximum Density Subgraph
Partitioning of VLSI circuits and systems
DAC '96 Proceedings of the 33rd annual Design Automation Conference
Circuit clustering using graph coloring
ISPD '99 Proceedings of the 1999 international symposium on Physical design
Edge separability based circuit clustering with application to circuit partitioning
ASP-DAC '00 Proceedings of the 2000 Asia and South Pacific Design Automation Conference
Performance-driven multi-level clustering with application to hierarchical FPGA mapping
Proceedings of the 38th annual Design Automation Conference
Efficient circuit clustering for area and power reduction in FPGAs
FPGA '02 Proceedings of the 2002 ACM/SIGDA tenth international symposium on Field-programmable gate arrays
Fine granularity clustering for large scale placement problems
Proceedings of the 2003 international symposium on Physical design
Optimality, scalability and stability study of partitioning and placement algorithms
Proceedings of the 2003 international symposium on Physical design
Q-Cut - Dynamic Discovery of Sub-goals in Reinforcement Learning
ECML '02 Proceedings of the 13th European Conference on Machine Learning
Wire length prediction based clustering and its application in placement
Proceedings of the 40th annual Design Automation Conference
The complexity of detecting fixed-density clusters
Discrete Applied Mathematics
Finding bipartition respecting natural dense clusters
ICC'05 Proceedings of the 9th International Conference on Circuits
A polynomial algorithm for partitioning problems
ACM Transactions on Embedded Computing Systems (TECS)
The complexity of detecting fixed-density clusters
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
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Top-down partitioning has focused on minimum cut or ratio cut objectives, while bottom-up clustering has focused on density-based objectives. In seeking a more unified perspective, we propose a new sum of densities measure for multi-way circuit decomposition, where the density of a subhypergraph is the ratio of the number of edges to the number of nodes in the subhypergraph. Finding a k-way partition that maximizes the sum of k subhypergraph densities is NP-hard, but an efficient flow-based method can find the optimal (maximum-density) subhypergraph in a given hypergraph. Based on this method, we develop a heuristic which in practice has less than 10% error from an optimal sum of densities decomposition. Other results suggest that density-based heuristics can capture cut-based objectives, whereas the converse would seem difficult.