Proceedings ArticleDOI
Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
Rajsekar Manokaran,Joseph (Seffi) Naor,Prasad Raghavendra,Roy Schwartz +3 more
- pp 11-20
TLDR
This work converts linear programming integrality gaps for the Multiway Cut, 0-Extension, and and Metric Labeling problems into UGC-based hardness results and suggests that if the unique games conjecture is true then a linear relaxation of the latter problems studied in several papers yields the best possible approximation.Abstract:
The connection between integrality gaps and computational hardness of discrete optimization problems is an intriguing question. In recent years, this connection has prominently figured in several tight UGC-based hardness results. We show in this paper a direct way of turning integrality gaps into hardness results for several fundamental classification problems. Specifically, we convert linear programming integrality gaps for the Multiway Cut, 0-Extension, and and Metric Labeling problems into UGC-based hardness results. Qualitatively, our result suggests that if the unique games conjecture is true then a linear relaxation of the latter problems studied in several papers (so-called earthmover linear program) yields the best possible approximation. Taking this a step further, we also obtain integrality gaps for a semi-definite programming relaxation matching the integrality gaps of the earthmover linear program. Prior to this work, there was an intriguing possibility of obtaining better approximation factors for labeling problems via semi-definite programming.read more
Citations
More filters
Journal ArticleDOI
Subexponential Algorithms for Unique Games and Related Problems
TL;DR: A sub exponential time approximation algorithm for the Unique Games problem that is exponential in an arbitrarily small polynomial of the input size, n, and shows that for every $\epsilon>0$ and every regular $n$-vertex graph~$G, one can break into disjoint parts so that the stochastic adjacency matrix of the induced graph on each part has at most n eigenvalues larger than $1-\eta.
Proceedings ArticleDOI
Beating the Random Ordering is Hard: Inapproximability of Maximum Acyclic Subgraph
TL;DR: This work studies max.
Proceedings ArticleDOI
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
Prasad Raghavendra,David Steurer +1 more
TL;DR: It is implied that including any valid constraints on up to up to $\exp(\log\log~n)^{1/4})$ vectors to natural semidefinite program, does not improve the approximation ratio for any problem in the following classes: constraint satisfaction problems, ordering constraints satisfaction problems and metric labeling problems over constant-size metrics.
Proceedings ArticleDOI
On the Unique Games Conjecture (Invited Survey)
TL;DR: This article surveys recently discovered connections between the Unique Games Conjecture and computational complexity, algorithms, discrete Fourier analysis, and geometry.
Proceedings ArticleDOI
On the unique games conjecture
TL;DR: This article surveys recently discovered connections between the Unique Games Conjecture and computational complexity, algorithms, discrete Fourier analysis, and geometry.
References
More filters
Journal ArticleDOI
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
TL;DR: This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
Proceedings ArticleDOI
On the power of unique 2-prover 1-round games
TL;DR: The main idea is to use the 2-prover game given by the Unique Games Conjecture as an "outer verifier" and build new probabilistically checkable proof systems (PCPs) on top of it.
Journal ArticleDOI
Vertex cover might be hard to approximate to within 2-ε
Subhash Khot,Oded Regev +1 more
TL;DR: In this paper, it was shown that vertex cover is hard to approximate within any constant factor better than 2 on k-uniform hypergraphs, which is the same conjecture as in this paper.
Journal ArticleDOI
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
TL;DR: This paper shows a reduction from the Unique Games problem to the problem of approximating MAX-CUT to within a factor of $\alpha_{\text{\tiny{GW}}} + \epsilon$ for all $\ep silon > 0$, and indicates that the geometric nature of the Goemans-Williamson algorithm might be intrinsic to the MAX- CUT problem.
Proceedings ArticleDOI
On approximating arbitrary metrices by tree metrics
TL;DR: A generation algorithm for the random generation of models of amorphous strutures, which can be modeled as graphs which see embedded in d-space, using the well known approach of simulating a rapidly-mixing Markov chain.