Abstract
We give approximation algorithms for the edge expansion and sparsest cut with product demands problems on directed hypergraphs, which subsume previous graph models such as undirected hypergraphs and directed normal graphs.
Using an SDP formulation adapted to directed hypergraphs, we apply the SDP primal-dual framework by Arora and Kale (JACM 2016) to design polynomial-time algorithms whose approximation ratios match those of algorithms previously designed for more restricted graph models. Moreover, we have deconstructed their framework and simplified the notation to give a much cleaner presentation of the algorithms.
The full version of this paper is available online [6].
T.-H. H. Chan—This work was partially supported by the Hong Kong RGC under the grant 17200817.
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Notes
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- 2.
In the original notation [9, p. 59], the claimed constraint is \(\mathbf {Tr}(\mathbf {X}) \le n\), but for general cut S, only the weaker bound \(\mathbf {Tr}(\mathbf {X}) \le \varTheta (n^2)\) holds.
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Chan, TH.H., Sun, B. (2018). SDP Primal-Dual Approximation Algorithms for Directed Hypergraph Expansion and Sparsest Cut with Product Demands. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_57
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DOI: https://doi.org/10.1007/978-3-319-94776-1_57
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