A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Randomized algorithms
Approximating clique and biclique problems
Journal of Algorithms
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
Greedily finding a dense subgraph
Journal of Algorithms
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Monte Carlo algorithm for fast projective clustering
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Complexity of finding dense subgraphs
Discrete Applied Mathematics
Fast Algorithms for Mining Association Rules in Large Databases
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Approximating Maximum Clique by Removing Subgraphs
SIAM Journal on Discrete Mathematics
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Dense subgraph problems with output-density conditions
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Maximum dispersion problem in dense graphs
Operations Research Letters
Efficient diversity-aware search
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
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We consider the dense subgraph problem that extracts a subgraph, with a prescribed number of vertices, having the maximum number of edges (or total edge weight, in the weighted case) in a given graph. We give approximation algorithms with improved theoretical approximation ratios assuming that the density of the optimal output subgraph is high, where density is the ratio of number of edges (or sum of edge weights) to the number of edges in the clique on the same number of vertices. Moreover, we investigate the case where the input graph is bipartite and design a randomized pseudopolynomial time approximation scheme that can become a randomized PTAS, even if the size of the optimal output graph is comparatively small. This is a significant improvement in a theoretical sense, since no constant-ratio approximation algorithm was known previously if the output graph has o(n) vertices.