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2012
ACM

Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph

9 years 8 months ago
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
The Densest k-subgraph problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant gap between known upper and lower bounds for Densest k-subgraph: the current best algorithm gives an ≈ O(n1/4 ) approximation, while even showing a small constant factor hardness requires significantly stronger assumptions than P = NP. In addition to interest in designing better algorithms, a number of recent results have exploited the conjectured hardness of Densest ksubgraph and its variants. Thus, understanding the approximability of Densest k-subgraph is an important challenge. In this work, we give evidence for the hardness of approximating Densest k-subgraph within polynomial factors. Specifically, we expose the limitations of strong semidefinite programs from SDP hierarchies in solving Densest k-subgraph. Our results include: • A lower bound of Ω n1/4 / log3 n on the integrality gap for Ω(log...
Aditya Bhaskara, Moses Charikar, Aravindan Vijayar
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where SODA
Authors Aditya Bhaskara, Moses Charikar, Aravindan Vijayaraghavan, Venkatesan Guruswami, Yuan Zhou
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