Detecting high log-densities - An O(n1/4) approximation for densest k-subgraph

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2010, Pages 201-210

  Bhaskara, Aditya ^a   Charikar, Moses ^a   Chlamtac, Eden ^b   Feige, Uriel ^b   Vijayaraghavan, Aravindan ^a  

^a PRINCETON UNIVERSITY   (United States)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

approximation algorithm; densest k subgraph; lp hierarchies; random planted model

Indexed keywords

APPROXIMATION RATIOS; AVERAGE DEGREE; AVERAGE-CASE; BEST-KNOWN ALGORITHMS; DENSEST K SUBGRAPH; EIGEN-VALUE; GRAPH G; LP HIERARCHIES; NP-HARD; PARAMETER RANGE; POLYNOMIAL-TIME; RANDOM GRAPHS; RANDOM INSTANCE; SUBEXPONENTIAL TIME; SUBGRAPH PROBLEMS; SUBGRAPHS; UPPER AND LOWER BOUNDS;

AGRICULTURE; COMPUTATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; POLYNOMIAL APPROXIMATION;

APPROXIMATION ALGORITHMS;

EID: 77954702542     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1806689.1806719     Document Type: Conference Paper

References (18)

1. N. Alon, M. Krivelevich, and B. Sudakov. Finding a large hidden clique in a random graph. pages 457-466, 1998.
2. N. Alon and J. Spencer. The Probabilistic Method. Wiley-Interscience, third edition, 2008.
3. B. Applebaum, B. Barak, and A. Wigderson. Public key cryptography from different assumptions. Preliminary version as cryptology eprint report 2008/335 by Barak and Wigderson, 2008.
4. S. Arora, B. Barak, M. Brunnermeier, and R. Ge. Computational complexity and information asymmetry in financial products. In Proceedings of the First Symposium on Innovations in Computer Science (ICS), 2010.
5. Y. Asahiro, R. Hassin, and K. Iwama. Complexity of finding dense subgraphs. Discrete Appl. Math., 121(1-3):15-26, 2002.
6. 1/4) approximation for densest k-subgraph. CoRR, abs/1001.2891, 2010.
7. B. E. Birnbaum and K. J. Goldman. An improved analysis for a greedy remote-clique algorithm using factor-revealing LPs. Algorithmica, 1:42-59, 2009.
8. M. Charikar, M. Hajiaghayi, and H. J. Karloff. Improved approximation algorithms for label cover problems. In ESA, volume 5757 of Lecture Notes in Computer Science, pages 23-34. Springer, 2009.
9. U. Feige. Relations between average case complexity and approximation complexity. In Proceedings of the 34th annual ACM Symposium on Theory of Computing (STOC'02), pages 534-543. ACM Press, 2002.
10. U. Feige, G. Kortsarz, and D. Peleg. The dense k-subgraph problem. Algorithmica, 29(3):410-421, 2001.
11. U. Feige and M. Langberg. Approximation algorithms for maximization problems arising in graph partitioning. J. Algorithms, 41(2):174-211, 2001.
12. U. Feige and M. Seltser. On the densest k-subgraph problems. Technical Report CS97-16, Weizmann Institute of Science, Rehovot, Israel, 1997.
13. Z. Füredi and J. Komlós. The eigenvalues of random symmetric matrices. Combinatorica, 1:233-241, 1981.
14. G. Gallo, M. D. Grigoriadis, and R. E. Tarjan. A fast parametric maximum flow algorithm and applications. SIAM J. Comput., 18(1):30-55, 1989.
15. D. Goldstein and M. Langberg. The dense k subgraph problem. CoRR, abs/0912.5327, 2010.
16. S. Khot. Ruling out PTAS for graph min-bisection, densest subgraph and bipartite clique. In Proceedings of the 44th Annual IEEE Symposium on the Foundations of Computer Science (FOCS'04), pages 136-145, 2004.
17. L. Lovász and A. Schrijver. Cones of matrices and set-functions and 0-1 optimization. SIAM Journal on Optimization, 1:166-190, 1991.
18. A. Srivastav and K. Wolf. Finding dense subgraphs with semidefinite programming. In Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX), pages 181-191, 1998.