Hypergraph Partitioning for VLSI: Benchmarks, Code and Leaderboard

Hypergraph Partitioning Leaderboard: Leaderboard of minimum hyperedge cut values for different testcases with multiple imbalance factors.

SpecPart: A Supervised Spectral Framework for Hypergraph Partitioning Solution Improvement
K-SpecPart: A Supervised Spectral Framework for Multi-way Hypergraph Partitioning Solution Improvement

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Description

This repository supports "Data, Benchmarking and Roadmapping" goals for the balanced hypergraph min-cut partitioning problem, which is central to chip design and the divide-and-conquer paradigm. The repository is a one-stop shop" that serves the following purposes.

1. We provide the ISPD98 benchmarks (with unit vertex weights and actual vertex weights) and Titan23 benchmarks in hMETIS format. To understand this format please refer to the hMETIS manual.
2. We provde open source code for the Julia implementation of a recent hypergraph partitioning code, SpecPart. We also provide the implementation of CMG (Combinatorial Multigrid) preconditioner with this package.
3. We provide open source code for the Julia implementation of K-SpecPart which is an enhancement over SpecPart, and can handle multi-way partitions. Comparison of cutsizes and runtimes are available here.
4. We provide the best known partitioning solutions (for number of partitions 2,3, and 4) for the ISPD98 benchmarks (both with unit vertex weights and actual vertex weights) and the Titan Benchmarks.
5. We provide a "Golden Evaluator" which processes a partition file to report the cutsize and the block balances.
6. We provide a leaderboard of minimum hyperedge cutsize values found on the ISPD98 benchmarks and the Titan23 benchmarks. We encourage fellow researchers to update the leaderboard if better solutions are found.

We hope to see pull requests with new solutions and optimization codes, and will continue to update the repository and leaderboard as we this happens.

Table of Contents

• Current file/directory tree and description
• (SpecPart-specific) installation and run instructions
• (K-SpecPart-specific) installation and run instructions
• Leaderboard of minimum hyperedge cutsize values
  • Leaderboard for number of partitions = 2
  • Leaderboard for number of partitions = 3
  • Leaderboard for number of partitions = 4
• Authors

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Current File/Directory Tree and Description

.
├── SpecPart                              # SpecPart Implementation
│   ├── SpectralCommunityDetection
│   │   ├── cmg                           # Combinatorial Multigrid Implementation
|
├── benchmark                             # hypergraph files for each benchmark
│   ├── ISPD_benchmark                    # ISPD98 VLSI Circuit Benchmark Suite with unit vertex weights
│   ├── ISPD_weight_benchmark             # ISPD98 VLSI Circuit Benchmark Suite with actual vertex weights
│   └── Titan23_benchmark                 # Titan23 Benchmark Suite
│   
├── golden_evaluator                      # script for evaluating partitioning solutions
│ 
├── solutions_2way                        # 2-way solutions for all the benchmarks with different imbalance factors
│   ├── ISPD_benchmark_solutions          # solutions on ISPD98 testcases with unit vertex weights
│   |   ├── hMetis                        # solutions using hMETIS
│   |   |   ├── UBfactor_2                # solutions with imbalance factor 2
│   |   |   └── UBfactor_10               # solutions with imbalance factor 10
│   |   |   
│   |   ├── KaHyPar                       # solutions with KaHyPar
│   |   |   ├── UBfactor_2                # solutions with imbalance factor 2
│   |   |   └── UBfactor_10               # solutions with imbalance factor 10
│   |   |   
|   |   └── SpecPart                      # solutions with SpecPart
│   |       ├── hMetis_SpecPart           # SpecPart with initial solution generated from hMETIS
|   │       |   ├── UBfactor_2            # solutions with imbalance factor 2
│   |       |   └── UBfactor_10           # solutions with imbalance factor 10
│   |       |
│   |       └── KaHyPar_SpecPart          # SpecPart with initial solution generated from KaHyPar
|   │           ├── UBfactor_2            # solutions with imbalance factor 2
│   |           └── UBfactor_10           # solutions with imbalance factor 10
│   |       
│   ├── ISPD_weight_benchmark_solutions   # solutions on ISPD98 testcases with actual vertex weights
│   |   ├── hMetis                        # solutions with hMETIS
│   |   |   ├── UBfactor_2                # solutions with imbalance factor 2
│   |   |   └── UBfactor_10               # solutions with imbalance factor 10
│   |   |   
│   |   ├── KaHyPar                       # solutions with KaHyPar
│   |   |   ├── UBfactor_2                # solutions with imbalance factor 2
│   |   |   └── UBfactor_10               # solutions with imbalance factor 10
│   |   |   
│   |   └── SpecPart                      # solutions with SpecPart
│   |       ├── hMetis_SpecPart           # SpecPart with initial solution generated from hMETIS
|   │       |   ├── UBfactor_2            # solutions with imbalance factor 2
│   |       |   └── UBfactor_10           # solutions with imbalance factor 10
│   |       |   
│   |       └── KaHyPar_SpecPart          # SpecPart with initial solution generated from KaHyPar
|   │           ├── UBfactor_2            # solutions with imbalance factor 2
│   |           └── UBfactor_10           # solutions with imbalance factor 10
│   |       
└── └── Titan23_benchmark_solutions       # solutions on Titan23 testcases
│        ├── hMetis                       # solutions with hMETIS
│        |   ├── UBfactor_2               # solutions with imbalance factor 2
│        |   └── UBfactor_20              # solutions with imbalance factor 20
│        |   
│        ├── hMetis_Autotune              # solutions with Autotuned hMETIS
│        |   └── UBfactor_10              # solutions with imbalance factor 10
│        |   
│        ├── hMetis_Autotune_SpecPart     # SpecPart with initial solution generated from Autotuned hMETIS   
│        |   └── UBfactor_10              # solutions with imbalance factor 10
│        |   
│        └── hMetis_SpecPart              # SpecPart with initial solution generated from hMETIS   
│            ├── UBfactor_2               # solutions with imbalance factor 2
│            └── UBfactor_20              # solutions with imbalance factor 20
├── solutions_k_way                        # K-way solutions for all the benchmarks with different imbalance factors
│   ├── ISPD_benchmark_solutions          # K-way solutions on ISPD98 testcases with unit vertex weights  
│   ├── ISPD_weight_benchmark_solutions   # K-way solutions on ISPD98 testcases with actual vertex weights    
└── └── Titan23_benchmark_solutions       # K-way solutions on Titan23 testcases
        └── hMetis_SpecPart               # SpecPart with initial solution generated from hMETIS 
            ├── 3way                      # 3-way solutions
            |   └── UBfactor_2            # 3-way solutions with imbalance factor 2
            └── 4way                      # 4-way solutions
                └── UBfactor_2            # 4-way solutions with imbalance factor 2

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Installation and Run Instructions

Open Julia REPL and do the following:

include("SpectralRefinement.jl")
using Main.SpecPart
SpecPart.SpectralRefinement(hg = "Hypergraph file", pfile = "Partition file", Nparts = "Number of partitions", cycles = ζ, hyperedges_threshold = γ, ub = ε, nev = m, refine_iters = β, best_solns = δ)

ζ is the number of graph cycles (we recommend ζ=2)
γ is the threshold number of hyperedges to run ILP (we recommend γ=600)
ε is the imbalance factor (ε=1-49)
m is the number of eigenvectors (we recommend m=2)
β is the number of SpecPart iterations (we recommend β=2)
δ is the number of solutions picked from candidate solutions for overlay based clustering (we recommend δ=5)

A user guide is available here.

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Leaderboards of minimum hyperedge cut values

Number of partitions 2

Current Leaderboard of minimum hyperedge cut values on ISPD98 testcases with unit vertex weights and actual vertex weights, with different imbalance factors (ε):

Testcase	Statistics		Cutsize
	# Vertices	# Hyperedges	ε = 1	ε = 2	ε = 5	ε = 10
IBM01	12752	14111	203	200	180	166
IBM01_wt	12752	14111	216	215	215	215
IBM02	19601	19584	341	307	262	262
IBM02_wt	19601	19584	266	266	260	207
IBM03	23136	27401	954	951	950	950
IBM03_wt	23136	27401	775	691	680	580
IBM04	27507	31970	580	573	514	388
IBM04_wt	27507	31970	496	475	438	393
IBM05	29347	28446	1719	1706	1697	1645
IBM05_wt	29347	28446	1724	1722	1693	1647
IBM06	32498	34826	976	962	871	728
IBM06_wt	32498	34826	483	442	363	297
IBM07	45926	48117	910	878	818	764
IBM07_wt	45926	48117	737	736	717	636
IBM08	51309	50513	1140	1140	1140	1120
IBM08_wt	51309	50513	1170	1168	1120	972
IBM09	53395	60902	625	620	620	519
IBM09_wt	53395	60902	519	519	519	522
IBM10	69429	75196	1285	1253	1244	1244
IBM10_wt	69429	75196	1030	947	732	413
IBM11	70558	81454	1065	1051	951	763
IBM11_wt	70558	81454	767	766	687	656
IBM12	71076	77240	1934	1919	1871	1841
IBM12_wt	71076	77240	1976	1973	1976	1855
IBM13	84199	99666	837	831	831	655
IBM13_wt	84199	99666	892	846	846	793
IBM14	147605	152772	1842	1842	1794	1509
IBM14_wt	147605	152772	1740	1674	1501	1282
IBM15	161570	186608	2743	2730	2530	2135
IBM15_wt	161570	186608	2014	1913	1771	1444
IBM16	183484	190048	1975	1827	1695	1619
IBM16_wt	183484	190048	1656	1634	1634	1634
IBM17	185495	189581	2314	2270	2186	1989
IBM17_wt	185495	189581	2302	2289	2187	2018
IBM18	210613	201920	1521	1521	1521	1520
IBM18_wt	210613	201920	1641	1588	1520	1520

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Current Leaderboard of minimum hyperedge cut values on Titan23 testcases with different imbalance factors (ε):

	Statistics		Cutsize
Testcase	#Vertices	#Hyperedges	ε = 1	ε = 2	ε = 5	ε = 10	ε = 20
sparcT1_core	91976	92827	1088	977	977	977	903
neuron	92290	125305	239	239	239	239	206
stereovision	94050	127085	186	169	169	91	91
des90	111221	139557	416	372	372	372	358
SLAM_spheric	113115	142408	1061	1061	1061	1061	1061
cholesky_mc	113250	144948	343	285	281	281	285
segmentation	138295	179051	165	118	107	85	78
bitonic_mesh	192064	235328	588	584	581	543	483
dart	202354	223301	807	788	788	719	540
openCV	217453	284108	566	481	481	481	481
stap_qrd	240240	290123	398	398	380	296	295
minres	261359	320540	241	215	215	199	189
cholesky_bdti	266422	342688	1213	1156	1156	1156	947
denoise	275638	356848	457	416	416	416	224
sparcT2_core	300109	302663	1227	1227	1227	1227	1227
gsm_switch	493260	507821	1836	1827	1615	1460	1407
mes_noc	547544	577664	703	634	634	634	617
LU230	574372	669477	3362	3273	3339	3262	2677
LU_Network	635456	726999	646	525	524	524	524
sparcT1_chip2	820886	821274	1037	899	899	815	783
directrf	931275	1374742	673	574	574	378	295
bitcoin_miner	1089284	1448151	1512	1297	1232	1232	1225

Number of partitions 3

Current Leaderboard of minimum hyperedge cut values on Titan23 testcases with imbalance factor (ε) = 2:

	Statistics		Cutsize
Testcase	#Vertices	#Hyperedges	ε = 2
sparcT1_core	91976	92827	1889
neuron	92290	125305	396
stereovision	94050	127085	336
des90	111221	139557	535
SLAM_spheric	113115	142408	2720
cholesky_mc	113250	144948	864
segmentation	138295	179051	453
bitonic_mesh	192064	235328	895
dart	202354	223301	1243
openCV	217453	284108	525
stap_qrd	240240	290123	497
minres	261359	320540	309
cholesky_bdti	266422	342688	1755
denoise	275638	356848	915
sparcT2_core	300109	302663	2249
gsm_switch	493260	507821	3694
mes_noc	547544	577664	1125
LU230	574372	669477	4548
LU_Network	635456	726999	882
sparcT1_chip2	820886	821274	1404
directrf	931275	1374742	762
bitcoin_miner	1089284	1448151	1917

Number of partitions 4

Current Leaderboard of minimum hyperedge cut values on Titan23 testcases with different imbalance factors (ε):

	Statistics		Cutsize
Testcase	#Vertices	#Hyperedges	ε = 2
sparcT1_core	91976	92827	2942
neuron	92290	125305	431
stereovision	94050	127085	475
des90	111221	139557	747
SLAM_spheric	113115	142408	3241
cholesky_mc	113250	144948	984
segmentation	138295	179051	490
bitonic_mesh	192064	235328	1311
dart	202354	223301	1401
openCV	217453	284108	522
stap_qrd	240240	290123	674
minres	261359	320540	407
cholesky_bdti	266422	342688	1865
denoise	275638	356848	1001
sparcT2_core	300109	302663	3558
gsm_switch	493260	507821	4404
mes_noc	547544	577664	1346
LU230	574372	669477	6310
LU_Network	635456	726999	1417
sparcT1_chip2	820886	821274	1601
directrf	931275	1374742	1092
bitcoin_miner	1089284	1448151	2737

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Authors

Ismail Bustany, Andrew Kahng, Yiannis Koutis, Bodhisatta Pramanik, Zhiang Wang

References

To reference SpecPart, please cite:

I. Bustany, A. B. Kahng, Y. Koutis, B. Pramanik and Z. Wang, "SpecPart: A Supervised Spectral Framework for Hypergraph Partitioning Solution Improvement", (pdf), Proc. ACM/IEEE International Conference on Computer-Aided Design, 2022.

Acknowledgments

This work was partially supported by NSF CCF-2112665, CCF-2039863, CCF-1813374, DARPA HR0011-18-0-2-0032