Conditions beyond treewidth for tightness of higher-order LP relaxations
Conditions beyond treewidth for tightness of higher-order LP relaxations
复制标题
高阶 LP 松弛的严格性超出树宽的条件
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Adrian Weller
中科院分区：
文献类型：
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作者：
Mark Rowland;Aldo Pacchiano;Adrian Weller
线性规划（LP）松弛是试图找到离散图形模型的最可能配置的流行方法。如果松弛问题的解是在积分顶点处得到的，那么该解保证是精确的，我们说松弛是紧的。我们认为二进制成对模型，并引入新的方法，使我们能够证明完善的条件，在Sherali-Adams层次的LP松弛的紧密性。我们的研究结果表明，高阶LP松弛，树宽是不完全正确的方式来表征紧密性。这项工作主要是理论性的，具有可以提高实践效率的见解。
Linear programming (LP) relaxations are a popular method to attempt to find a most likely configuration of a discrete graphical model. If a solution to the relaxed problem is obtained at an integral vertex then the solution is guaranteed to be exact and we say that the relaxation is tight. We consider binary pairwise models and introduce new methods which allow us to demonstrate refined conditions for tightness of LP relaxations in the Sherali-Adams hierarchy. Our results include showing that for higher order LP relaxations, treewidth is not precisely the right way to characterize tightness. This work is primarily theoretical, with insights that can improve efficiency in practice.
DOI：
10.1016/j.artint.2011.02.003
发表时间：
2010-08
期刊：
Artif. Intell.
影响因子：
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作者：
Martin C. Cooper;Stanislav Živný
通讯作者：
Martin C. Cooper;Stanislav Živný