Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Greedily finding a dense subgraph
Journal of Algorithms
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
A constant approximation algorithm for the densest k-subgraph problem on chordal graphs
Information Processing Letters
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
Densest k-subgraph approximation on intersection graphs
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
On the k-edge-incident subgraph problem and its variants
Discrete Applied Mathematics
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Given an interval graph and integer k, we consider the problem of finding a subgraph of size k with a maximum number of induced edges, called densest k-subgraph problem in interval graphs. It has been shown that this problem is NP-hard even for chordal graphs [17], and there is probably no PTAS for general graphs [12]. However, the exact complexity status for interval graphs is a long-standing open problem [17], and the best known approximation result is a 3-approximation algorithm [16]. We shed light on the approximation complexity of finding a densest k-subgraph in interval graphs by presenting a polynomialtime approximation scheme (PTAS), that is, we show that there is an (1+ε)-approximation algorithm for any ε 0, which is the first such approximation scheme for the densest k-subgraph problem in an important graph class without any further restrictions.