Breaking the rectangle bound barrier against formula size lower bounds

Authors:
Kenya Ueno
Affiliations:
The Young Researcher Development Center and Graduate School of Informatics, Kyoto University
Venue:
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Year:
2010

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Abstract

Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LP-relaxation. As extensions of the LP bound, we introduce novel general techniques proving formula size lower bounds, named a quasi-additive bound and the Sherali-Adams bound. While the Sherali-Adams bound is potentially strong enough to give a lower bound matching to the rectangle bound, we prove that the quasi-additive bound can surpass the rectangle bound.