On division versus saturation in pseudo-boolean solving
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Standard
On division versus saturation in pseudo-boolean solving. / Gocht, Stephan; Nordström, Jakob; Yehudayoff, Amir.
Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019. ed. / Sarit Kraus. International Joint Conferences on Artificial Intelligence, 2019. p. 1711-1718.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - GEN
T1 - On division versus saturation in pseudo-boolean solving
AU - Gocht, Stephan
AU - Nordström, Jakob
AU - Yehudayoff, Amir
PY - 2019
Y1 - 2019
N2 - The conflict-driven clause learning (CDCL) paradigm has revolutionized SAT solving over the last two decades. Extending this approach to pseudo-Boolean (PB) solvers doing 0-1 linear programming holds the promise of further exponential improvements in theory, but intriguingly such gains have not materialized in practice. Also intriguingly, most PB extensions of CDCL use not the division rule in cutting planes as defined in [Cook et al.,'87] but instead the so-called saturation rule. To the best of our knowledge, there has been no study comparing the strengths of division and saturation in the context of conflict-driven PB learning, when all linear combinations of inequalities are required to cancel variables. We show that PB solvers with division instead of saturation can be exponentially stronger. In the other direction, we prove that simulating a single saturation step can require an exponential number of divisions. We also perform some experiments to see whether these phenomena can be observed in actual solvers. Our conclusion is that a careful combination of division and saturation seems to be crucial to harness more of the power of cutting planes.
AB - The conflict-driven clause learning (CDCL) paradigm has revolutionized SAT solving over the last two decades. Extending this approach to pseudo-Boolean (PB) solvers doing 0-1 linear programming holds the promise of further exponential improvements in theory, but intriguingly such gains have not materialized in practice. Also intriguingly, most PB extensions of CDCL use not the division rule in cutting planes as defined in [Cook et al.,'87] but instead the so-called saturation rule. To the best of our knowledge, there has been no study comparing the strengths of division and saturation in the context of conflict-driven PB learning, when all linear combinations of inequalities are required to cancel variables. We show that PB solvers with division instead of saturation can be exponentially stronger. In the other direction, we prove that simulating a single saturation step can require an exponential number of divisions. We also perform some experiments to see whether these phenomena can be observed in actual solvers. Our conclusion is that a careful combination of division and saturation seems to be crucial to harness more of the power of cutting planes.
UR - http://www.scopus.com/inward/record.url?scp=85074915020&partnerID=8YFLogxK
U2 - 10.24963/ijcai.2019/237
DO - 10.24963/ijcai.2019/237
M3 - Article in proceedings
AN - SCOPUS:85074915020
SP - 1711
EP - 1718
BT - Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
A2 - Kraus, Sarit
PB - International Joint Conferences on Artificial Intelligence
T2 - 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
Y2 - 10 August 2019 through 16 August 2019
ER -
ID: 251867307