Approximation algorithms for NP-hard problems
PCP characterizations of NP: towards a polynomially-small error-probability
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The budgeted maximum coverage problem
Information Processing Letters
On the red-blue set cover problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Two Formal Analys s of Attack Graphs
CSFW '02 Proceedings of the 15th IEEE workshop on Computer Security Foundations
Automated Generation and Analysis of Attack Graphs
SP '02 Proceedings of the 2002 IEEE Symposium on Security and Privacy
On the hardness of approximating label-cover
Information Processing Letters
Hi-index | 0.00 |
We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t , the edges of G are classified into different categories, represented by a set of labels . The labels may also have weights. We want to pick a subset of labels of minimum cardinality (or minimum total weight), such that the removal of all edges with these labels disconnects s and t . We give the first non-trivial approximation and hardness results for the Label Cut problem. Firstly, we present an $O(\sqrt{m})$-approximation algorithm for the Label Cut problem, where m is the number of edges in the input graph. Secondly, we show that it is NP-hard to approximate Label Cut within $2^{\log ^{1 - 1/\log\log^c n} n}$ for any constant c n is the input length of the problem. Thirdly, our techniques can be applied to other previously considered optimization problems. In particular we show that the Minimum Label Path problem has the same approximation hardness as that of Label Cut, simultaneously improving and unifying two known hardness results for this problem which were previously the best (but incomparable due to different complexity assumptions).