A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Greedily Finding a Dense Subgraph
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
On the densest k-subgraph problems
On the densest k-subgraph problems
Approximation algorithms for maximum dispersion
Operations Research Letters
Maximum dispersion problem in dense graphs
Operations Research Letters
Upper bounds and exact algorithms for p-dispersion problems
Computers and Operations Research
The complexity of detecting fixed-density clusters
Discrete Applied Mathematics
The inverse protein folding problem on 2D and 3D lattices
Discrete Applied Mathematics
Dense subgraph problems with output-density conditions
ACM Transactions on Algorithms (TALG)
Finding Dense Subgraphs with Size Bounds
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Enumeration of isolated cliques and pseudo-cliques
ACM Transactions on Algorithms (TALG)
Upper bounds and exact algorithms for p-dispersion problems
Computers and Operations Research
The complexity of detecting fixed-density clusters
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
Linear-time enumeration of isolated cliques
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Dense subgraph problems with output-density conditions
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Dense Neighborhoods on Affinity Graph
International Journal of Computer Vision
Computer Science Review
A polyhedral study of the maximum edge subgraph problem
Discrete Applied Mathematics
Approximation algorithms for the sex-equal stable marriage problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Dense subgraphs on dynamic networks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
View-Invariant object detection by matching 3d contours
ACCV'12 Proceedings of the 11th international conference on Computer Vision - Volume 2
Denser than the densest subgraph: extracting optimal quasi-cliques with quality guarantees
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Truncated power method for sparse eigenvalue problems
The Journal of Machine Learning Research
| Hi-index | 0.04 |
The k-f(k) dense subgraph problem ((k, f(k))-DSP) asks whether there is a k-vertex subgraph of a given graph G which has at least f(k) edges. When f(k)=k(k - 1)/2, (k,f(k))-DSP is equivalent to the well-known k-clique problem. The main purpose of this paper is to discuss the problem of finding slightly dense subgraphs. Note that f(k) is about k2 for the k-clique problem. It is shown that (k,f(k))-DSP remains NP-complete for f(k)= Θ(k1+ε) where ε may be any constant such that 0 (k, f(k))-DSP is NP-complete for f(k)= ek2/υ2(1 +O(υε-1)), where υ is the number of G's vertices and e is the number of G's edges. This condition is quite tight because the answer to (k, f(k))-DSP is always yes for f(k)= ek2/υ2(1 -(υ- k)/(υk- k)) that is the average number of edges in a subgraph of k vertices. Also, we show that the hardness of (k, f(k))-DSP remains for regular graphs: (k, f(k))-DSP is NP-complete for Θ(υε1)-regular graphs if f(k)= Θ(k1-ε2) for any 0 1, ε2