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- W4287331374 abstract "Given an undirected graph, the Densest-k-Subgraph problem (DkS) seeks to find a subset of k vertices such that the sum of the edge weights in the corresponding subgraph is maximized. The problem is known to be NP-hard, and is also very difficult to approximate, in the worst-case. In this paper, we present a new convex relaxation for the problem. Our key idea is to reformulate DkS as minimizing a submodular function subject to a cardinality constraint. Exploiting the fact that submodular functions possess a convex, continuous extension (known as the Lov'asz extension), we propose to minimize the Lov'asz extension over the convex hull of the cardinality constraints. Although the Lov'asz extension of a submodular function does not admit an analytical form in general, for DkS we show that it does. We leverage this result to develop a highly scalable algorithm based on the Alternating Direction Method of Multipliers (ADMM) for solving the relaxed problem. Coupled with a pair of fortuitously simple rounding schemes, we demonstrate that our approach outperforms existing baselines on real-world graphs and can yield high quality sub-optimal solutions which typically are a posteriori no worse than 65-80% of the optimal density." @default.
- W4287331374 created "2022-07-25" @default.
- W4287331374 creator A5002204846 @default.
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- W4287331374 date "2021-02-05" @default.
- W4287331374 modified "2023-09-29" @default.
- W4287331374 title "Exploring the Subgraph Density-Size Trade-off via the Lov'asz Extension" @default.
- W4287331374 doi "https://doi.org/10.48550/arxiv.2102.03434" @default.
- W4287331374 hasPublicationYear "2021" @default.
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