An Exact Algorithm for Minimum Vertex Cover Problem
Abstract
:1. Introduction
2. Basic Definition and Notation
3. EMVC Algorithm for Solving the MVC Problem
Algorithm 1: The EMVC algorithm (). |
4. Two Novel Lower Bounds for the MVC Problem
4.1. DegLB: The Degree-Based Lower Bound for MVC
4.2. SatLB: The Max-SAT-Based Lower Bound for MVC
- Every clause (other than the unit clause itself) containing l is removed;
- In every clause that contains , this literal is deleted.
5. Experimental Results
6. Summary and Future Work
Author Contributions
Funding
Conflicts of Interest
References
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Instance | EMVCTime | SBMSTime | FastVCBest | FastVCAvgt | |
---|---|---|---|---|---|
brock400-1 | 393 | 1.58 | - | 393 | 0.02 |
brock400-2 | 392 | 1.54 | - | 392 | 0.03 |
brock400-3 | 393 | 1.55 | - | 393 | 0.02 |
brock400-4 | 393 | 1.55 | 360.50 | 393 | 0.01 |
C250-9 | 245 | 0.15 | 14.11 | 245 | 0.01 |
C500-9 | 495 | 1.41 | - | 495 | 0.10 |
C1000-9 | 994 | 8.89 | - | 994 | 1.81 |
C2000-9 | 1994 | 78.33 | - | 1994 | 4.69 |
DSJC500-5 | 487 | 177.73 | - | 487 | 4.15 |
DSJC1000-5 | - | - | - | 986 | 48.91 |
gen400-p0-9-55 | 392 | 0.37 | 72.99 | 392 | <0.01 |
gen400-p0-9-65 | 393 | 0.38 | - | 393 | <0.01 |
gen400-p0-9-75 | 394 | 0.37 | 46.59 | 394 | <0.01 |
hamming10-2 | 1022 | 3.50 | - | 1022 | 0.27 |
hamming10-4 | 1004 | 13.55 | - | 1004 | 0.05 |
hamming8-2 | 254 | 0.48 | - | 254 | 0.01 |
johnson32-2-4 | 465 | 0.64 | - | 465 | 0.03 |
keller5 | 745 | 2.38 | - | 745 | 0.02 |
keller6 | 3298 | 186.54 | - | 3298 | 1.45 |
MANN-a27 | 375 | 0.23 | 10.57 | 375 | 0.01 |
MANN-a45 | 1032 | 3.04 | - | 1032 | 0.12 |
MANN-a81 | 3318 | 114.15 | - | 3318 | 1.57 |
p-hat1000-3 | 989 | 177.51 | - | 991 ↑ | 0.03 |
p-hat1500-3 | - | - | - | 1489 | 35.87 |
p-hat300-1 | 292 | 0.56 | 93.12 | 292 | <0.01 |
p-hat300-3 | 291 | 0.62 | 154.61 | 291 | 0.01 |
p-hat500-3 | 490 | 4.34 | - | 493↑ | 0.14 |
p-hat700-3 | - | - | - | 638 | 0.01 |
san1000 | 933 | 10.25 | - | 933 | 0.02 |
san200-0-7-1 | 191 | 0.29 | - | 194 ↑ | 0.02 |
san400-0-5-1 | 368 | 0.75 | - | 368 | 0.01 |
san400-0-7-1 | 389 | 0.44 | - | 390↑ | 0.02 |
san400-0-7-2 | 385 | 0.44 | 231.90 | 385 | <0.01 |
san400-0-7-3 | 381 | 0.41 | 132.99 | 381 | <0.01 |
san400-0-9-1 | 395 | 0.45 | - | 395 | 0.01 |
sanr400-0-7 | 392 | 2.43 | - | 392 | 0.06 |
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Wang, L.; Hu, S.; Li, M.; Zhou, J. An Exact Algorithm for Minimum Vertex Cover Problem. Mathematics 2019, 7, 603. https://doi.org/10.3390/math7070603
Wang L, Hu S, Li M, Zhou J. An Exact Algorithm for Minimum Vertex Cover Problem. Mathematics. 2019; 7(7):603. https://doi.org/10.3390/math7070603
Chicago/Turabian StyleWang, Luzhi, Shuli Hu, Mingyang Li, and Junping Zhou. 2019. "An Exact Algorithm for Minimum Vertex Cover Problem" Mathematics 7, no. 7: 603. https://doi.org/10.3390/math7070603