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FOCS

2008

IEEE

2008

IEEE

We prove that approximating the Max Acyclic Subgraph problem within a factor better than 1/2 is Unique-Games hard. Speciﬁcally, for every constant ε > 0 the following holds: given a directed graph G that has an acyclic subgraph consisting of a fraction (1 − ε) of its edges, if one can eﬃciently ﬁnd an acyclic subgraph of G with more than (1/2 + ε) of its edges, then the UGC is false. Note that it is trivial to ﬁnd an acyclic subgraph with 1/2 the edges, by taking either the forward or backward edges in an arbitrary ordering of the vertices of G. The existence of a ρ-approximation algorithm for ρ > 1/2 has been a basic open problem for a while. Our result is the ﬁrst tight inapproximability result for an ordering problem. The starting point of our reduction is a directed acyclic subgraph (DAG) in which every cut is nearly-balanced in the sense that the number of forward and backward edges crossing the cut are nearly equal; such DAGs were constructed in [3]. Using...

Added |
29 May 2010 |

Updated |
29 May 2010 |

Type |
Conference |

Year |
2008 |

Where |
FOCS |

Authors |
Venkatesan Guruswami, Rajsekar Manokaran, Prasad Raghavendra |

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