Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Approximation algorithms for NP-hard problems
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Approximation algorithms
A Polynomial Approximation Algorithm for the Minimum Fill-In Problem
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Approximating the Minimum Chain Completion problem
Information Processing Letters
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A bipartite graph G = (A ∪ B,E) is called a chain graph if there exists an ordering p =〈 v1, v2, . . . vn 〉 of the vertices in A = {v1,..., vn} such that N(v1) ⊆ N(v2) . . . ⊆ N(vn). Here N(v) denotes the set of neighbors of the vertex v in G. We call the vertex-deletion problem corresponding to the class of chain graphs as the Minimum Chain VERTEX DELETION problem and the induced subgraph problem corresponding to chain graphs as the MAXIMUM INDUCED CHAIN SUBGRAPH problem. A weighted version of these problems is obtained by assigning positive weights on vertices and asking for a minimum weight deletion set to get into the class of chain graphs or asking for maximum weight induced chain subgraph. Using a rounding technique we show that the weighted version of MINIMUM CHAIN VERTEX DELETION, has a factor 2 approximation algorithm on bipartite graphs. We also give a factor 3/2 approximation algorithm for a weighted version of MAXIMUM INDUCED CHAIN SUBGRAPH on bipartite graphs. We also show that both these problems are APX-complete.