Approximation algorithms for semi-random partitioning problems
Approximation algorithms for semi-random partitioning problems
复制标题
半随机划分问题的近似算法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Aravindan Vijayaraghavan
中科院分区：
文献类型：
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作者：
K. Makarychev;Yury Makarychev;Aravindan Vijayaraghavan
在本文中，我们提出并研究了一个新的半随机模型的图划分问题。我们相信，它捕捉到了现实世界实例的许多属性。该模型比Feige和Kilian的半随机模型和Bui、Chaudhuri、Leighton和Sipser的种植随机模型更灵活。
我们开发了一个通用的框架来解决半随机的情况下，并将其应用到几个感兴趣的问题。我们提出了常数因子双准则近似算法的半随机情况下的平衡割，多割，最小未割，稀疏割和小集扩展问题。我们还展示了如何几乎恢复最优解，如果实例满足一个额外的扩展条件。我们的算法比之前研究的随机和半随机模型的大多数算法在更广泛的参数范围内工作。
此外，我们研究了一个新的种植代数扩展模型，并在此模型中开发了图划分问题的常数因子双准则近似算法。
In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real-world instances. The model is more flexible than the semi-random model of Feige and Kilian and planted random model of Bui, Chaudhuri, Leighton and Sipser.
We develop a general framework for solving semi-random instances and apply it to several problems of interest. We present constant factor bi-criteria approximation algorithms for semi-random instances of the Balanced Cut, Multicut, Min Uncut, Sparsest Cut and Small Set Expansion problems. We also show how to almost recover the optimal solution if the instance satisfies an additional expanding condition. Our algorithms work in a wider range of parameters than most algorithms for previously studied random and semi-random models.
Additionally, we study a new planted algebraic expander model and develop constant factor bi-criteria approximation algorithms for graph partitioning problems in this model.