NDLI: Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph

Content Provider	IEEE Xplore Digital Library
Author	Guruswami, V. Manokaran, R. Raghavendra, P.
Copyright Year	2008
Description	Author affiliation: Princeton Univ., Princeton, NJ (Manokaran, R.) \|\| Univ. of Washington, Seattle, WA (Guruswami, V.; Raghavendra, P.)
Abstract	We prove that approximating the max. acyclic subgraph problem within a factor better than 1/2 is unique games hard. Specifically, for every constant epsiv > 0 the following holds: given a directed graph G that has an acyclic subgraph consisting of a fraction (1-epsiv) of its edges, if one can efficiently find an acyclic subgraph of G with more than (1/2 + epsiv) 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 rho-approximation algorithmfor rho > 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 isa directed acyclic subgraph (DAG) in which every cut isnearly-balanced in the sense that the number of forward and backward edges crossing the cut are nearly equal; such DAGs were constructed by Charikar et al. Using this, we are able to study max. acyclic subgraph, which is a constraint satisfaction problem (CSP) over an unbounded domain, by relating it to a proxy CSP over a bounded domain. The latter is then amenable to powerful techniques based on the invariance principle. Our results also give a super-constant factor inapproximability result for the feedback arc set problem. Using our reductions, we also obtain SDP integrality gapsfor both the problems.
Starting Page	573
Ending Page	582
File Size	354614
Page Count	10
File Format	PDF
ISBN	9780769534367
ISSN	02725428
DOI	10.1109/FOCS.2008.51
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation algorithms Computer science User-generated content Mathematics integrality gaps maximum acyclic subgraph feedback arc set unique games conjecture hardness of approximation
Content Type	Text
Resource Type	Article

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