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The Quest for Strong Inapproximability Results with Perfect Completeness * †

Joshua Brakensiek, Venkatesan Guruswami
unpublished
This elegant picture, however, does not apply for CSP instances that are perfectly satisfiable, due to the imperfect completeness inherent in the UGC.  ...  We further supplement the above results with a proof that an "almost Unique" version of Label Cover can be approximated within a constant factor on satisfiable instances. 1998 ACM Subject Classification  ...  We would like to thank Elchanan Mossel for useful discussion on a generalization of an invariance principle. We would also like to thank anonymous reviewers for helpful comments.  ... 
fatcat:k455kan4ebbjdh5mykhjogj6za

The Hardness of 3-Uniform Hypergraph Coloring

Irit Dinur*, Oded Regev†, Clifford Smyth‡
2005 Combinatorica  
The covering complexity of PCP verifiers offers a promising route to getting stronger inapproximability results for some minimization problems, and in particular, (hyper)-graph coloring problems.  ...  This enables us to prove that for any constant c, it is NP-hard to color a 2-colorable 4-uniform hypergraph using just c colors, and also yields a super-constant inapproximability result under a stronger  ...  We next turn to applying this to get a strong inapproximability result for hypergraph coloring.  ... 
doi:10.1007/s00493-005-0032-4 fatcat:455einszcfcgncrd4ld62ukeyi

Hardness of Approximate Hypergraph Coloring

Venkatesan Guruswami, Johan Hastad, Madhu Sudan
2002 SIAM journal on computing (Print)  
The covering complexity of PCP verifiers offers a promising route to getting stronger inapproximability results for some minimization problems, and in particular, (hyper)-graph coloring problems.  ...  This enables us to prove that for any constant c, it is NP-hard to color a 2-colorable 4-uniform hypergraph using just c colors, and also yields a super-constant inapproximability result under a stronger  ...  We next turn to applying this to get a strong inapproximability result for hypergraph coloring.  ... 
doi:10.1137/s0097539700377165 fatcat:27gyvztwnvcwzm6k5gf3nwutge

The complexity of finding independent sets in bounded degree (hyper)graphs of low chromatic number [chapter]

Venkatesan Guruswami, Ali Kemal Sinop
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
Our specific results include the following (where ∆, a constant, is a bound on the degree, and n is the number of vertices): • NP-hardness of finding an independent set of size larger than O n log ∆ ∆  ...  We prove almost tight hardness results under randomized reductions for finding independent sets in bounded degree graphs and hypergraphs that admit a good coloring.  ...  Acknowledgments We thank Rishi Saket for useful discussions and for pointing us to the reference [3] on the pairwise independent distribution of Theorem 5.1.  ... 
doi:10.1137/1.9781611973082.125 dblp:conf/soda/GuruswamiS11 fatcat:gwwvoafbmvajreh6awqsoz7dva

d-To-1 Hardness of Coloring 3-Colorable Graphs with O(1) Colors

Venkatesan Guruswami, Sai Sandeep, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
We prove that the d-to-1 conjecture for any fixed d implies the hardness of coloring a 3-colorable graph with C colors for arbitrarily large integers C.  ...  Earlier, the hardness of O(1)-coloring a 4-colorable graphs is known under the 2-to-1 conjecture, which is the strongest in the family of d-to-1 conjectures, and the hardness for 3-colorable graphs is  ...  The canonical starting point for most strong inapproximability results is the Label Cover problem.  ... 
doi:10.4230/lipics.icalp.2020.62 dblp:conf/icalp/GuruswamiS20 fatcat:jlb2a77e25cvpcjwi7tbdklmja

Large-Scale Election Campaigns: Combinatorial Shift Bribery

Robert Bredereck, Piotr Faliszewski, Rolf Niedermeier, Nimrod Talmon
2016 The Journal of Artificial Intelligence Research  
, with a single bribery action.  ...  Nevertheless, we provide parameterized algorithms and approximation algorithms for natural restricted cases.  ...  Then, in Section 4.2, we present a series of strong hardness results covering all our classes of shift actions for very restrictive sets of parameters (for example, many of our results apply already to  ... 
doi:10.1613/jair.4927 fatcat:gcwvxkudgrgnvju24k67jgocxi

Inapproximability for VCG-Based Combinatorial Auctions [chapter]

Dave Buchfuhrer, Shaddin Dughmi, Hu Fu, Robert Kleinberg, Elchanan Mossel, Christos Papadimitriou, Michael Schapira, Yaron Singer, Chris Umans
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
In this paper, we prove the first computational-complexity inapproximability results for incentive-compatible mechanisms for combinatorial auctions.  ...  The existence of incentive-compatible, computationallyefficient mechanisms for combinatorial auctions with good approximation ratios is the paradigmatic problem in algorithmic mechanism design.  ...  Dobzinski and Nisan [16] tackled the problem of proving inapproximability results for VCG-based mechanisms by taking a communication complexity [42, 25] approach.  ... 
doi:10.1137/1.9781611973075.45 dblp:conf/soda/BuchfuhrerDFKMPSSU10 fatcat:si245d27rjcqhddhsupdytdrxy

Finding Most Compatible Phylogenetic Trees over Multi-State Characters

Tuukka Korhonen, Matti J"ärvisalo
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
However, in practical situations a perfect phylogeny rarely exists, motivating the maximum compatibility problem of finding the largest subset of characters admitting a perfect phylogeny.  ...  In the NP-hard perfect phylogeny problem the input is a set of taxa (species) and characters (attributes) on them, and the task is to find an evolutionary tree that describes the evolution of the taxa  ...  We generated 5 random instances for each of the combinations, resulting in a total of 640 instances.  ... 
doi:10.1609/aaai.v34i02.5514 fatcat:fk5w6mxlwregzjelswtyq4nrhq

Parameterized Complexity and Approximation Algorithms

D. Marx
2007 Computer journal  
We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type, and propose directions for future research.  ...  Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems.  ...  ACKNOWLEDGMENTS I would like to thank Mike Fellows for asking me to write this survey, and for the many ideas, comments, and references that were essential in compiling the material.  ... 
doi:10.1093/comjnl/bxm048 fatcat:6yukdt7tvja3jf76zyuxfm536q

Constant Factor Lasserre Integrality Gaps for Graph Partitioning Problems

Venkatesan Guruswami, Ali Kemal Sinop, Yuan Zhou
2014 SIAM Journal on Optimization  
This complements recent algorithmic results in Guruswami and Sinop (2011) which used the Lasserre hierarchy to give an approximation scheme for these problems (with runtime depending on the spectrum of  ...  between the known approximation algorithms and non-approximability results.  ...  Several of the known results on strong integrality gap results for many rounds of the Lasserre hierarchy, starting with Schoenebeck's remarkable construction [Sch08] , apply in situations where a corresponding  ... 
doi:10.1137/13093025x fatcat:mihce365nfem7jpk44cgl476re

Constant Factor Lasserre Integrality Gaps for Graph Partitioning Problems [article]

Venkatesan Guruswami, Ali Kemal Sinop, Yuan Zhou
2014 arXiv   pre-print
This complements recent algorithmic results in Guruswami and Sinop (2011) which used the Lasserre hierarchy to give an approximation scheme for these problems (with runtime depending on the spectrum of  ...  between the known approximation algorithms and non-approximability results.  ...  Several of the known results on strong integrality gap results for many rounds of the Lasserre hierarchy, starting with Schoenebeck's remarkable construction [Sch08] , apply in situations where a corresponding  ... 
arXiv:1202.6071v3 fatcat:ankt6qg7yvgmlonzx4eptheivi

Scaffolding Problems Revisited: Complexity, Approximation and Fixed Parameter Tractable Algorithms, and Some Special Cases

Mathias Weller, Annie Chateau, Clément Dallard, Rodolphe Giroudeau
2018 Algorithmica  
This paper is devoted to new results about the scaffolding problem, an integral problem of genome inference in bioinformatics.  ...  We propose negative and positive results, exploring the frontier between difficulty and tractability of computing and/or approximating a solution to the problem.  ...  Acknowledgements This work was supported by the Institut de Biologie Computationnelle 2 (ANR Projet Investissements d'Avenir en bioinformatique IBC).  ... 
doi:10.1007/s00453-018-0405-x fatcat:m6eaidpx6remvjglwfxd7mnybm

Probabilistically checkable proofs [chapter]

Madhu Sudan
2004 Computational Complexity Theory  
A folklore result shows that any PCP for an NP-complete language must use q ≥ 3 to attain perfect completeness.  ...  for NP with perfect completeness and soundness bounded away from 1, or in other words the PCP Theorem!  ... 
doi:10.1090/pcms/010/12 fatcat:4vhklk62eng4lacp5tpcexo4ve

Probabilistically checkable proofs

Madhu Sudan
2009 Communications of the ACM  
A folklore result shows that any PCP for an NP-complete language must use q ≥ 3 to attain perfect completeness.  ...  for NP with perfect completeness and soundness bounded away from 1, or in other words the PCP Theorem!  ... 
doi:10.1145/1467247.1467267 fatcat:jwhq2op7yvfvtfezwxxqlj43i4

Making Markets and Democracy Work: A Story of Incentives and Computing

Tuomas Sandholm
2003 International Joint Conference on Artificial Intelligence  
For example, market clearing technology with specialized search algorithms is enabling a form of interaction that I call expressive competition.  ...  Those computing, communication, and privacy issues are deeply intertwined with the economic incentive issues.  ...  Even for these protocols, determining whose votes to elicit is NP-complete, even with perfect suspicions about how the agents will vote.  ... 
dblp:conf/ijcai/Sandholm03 fatcat:dfjyxzzikjbp5puy4ts3qpzevu
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