DATE: | Wednesday, March 17th 2004. |

TIME: | 4:30 PM - 5:30 PM |

PLACE: | McConnel 320 |

TITLE: | Rank Bounds and Integrality Gaps for Cutting Planes Procedures |

SPEAKER: | Josh Buresh-Oppenheim, University of Toronto |

Cutting planes procedures are techniques for solving, or
approximating the solutions to, integer linear programs. As such,
they
are used in practice to attack NP-hard optimization problems. They
can
also be used to prove the unsatisfiability of CNF formulas. The most
common examples of such procedures, those defined by Gomory and
Chvatal
and by Lovasz and Schrijver, are applied in rounds. For a given
input,
the number of rounds needed to solve the integer linear program, or to
prove that the CNF is unsatisfiable, is called the rank of the input.
We
present a new technique for proving rank lower bounds for these
procedures
when viewed as proof systems for unsatisfiability. We use this
technique
to prove near-optimal rank bounds for Gomory-Chvatal and
Lovasz-Schrijver
proofs of several prominent unsatisfiable CNF examples, including
random
kCNF formulas and the Tseitin graph formulas. It follows from these
lower
bounds that a linear number of rounds of these procedures when applied
to
relaxations of integer linear programs is not sufficient for reducing
the
integrality gap.

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