Two-prover one-round proof systems: their power and their problems (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A new way of using semidefinite programming with applications to linear equations mod p
Journal of Algorithms
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hardness results for approximate hypergraph coloring
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hardness of approximate hypergraph coloring
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Error reduction by parallel repetition-the state of the art
Error reduction by parallel repetition-the state of the art
A new PCP outer verifier with applications to homogeneous linear equations and max-bisection
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Is constraint satisfaction over two variables always easy?
Random Structures & Algorithms
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Every 2-CSP allows nontrivial approximation
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Guest column: inapproximability results via Long Code based PCPs
ACM SIGACT News
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Unique Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On Non-Approximability for Quadratic Programs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Local versus global properties of metric spaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Near-optimal algorithms for unique games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the fourier tails of bounded functions over the discrete cube
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Hardness of cut problems in directed graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Information Processing Letters
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
Journal of Computer and System Sciences
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Theoretical Computer Science
The multi-multiway cut problem
Theoretical Computer Science
Complexity and approximation of the minimum recombinant haplotype configuration problem
Theoretical Computer Science
Polynomial flow-cut gaps and hardness of directed cut problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Low-degree tests at large distances
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Near-optimal algorithms for maximum constraint satisfaction problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
The UGC hardness threshold of the ℓp Grothendieck problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms
Random Structures & Algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Approximating maximum satisfiable subsystems of linear equations of bounded width
Information Processing Letters
Parallel repetition in projection games and a concentration bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Some topics in analysis of boolean functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Improved Approximation Guarantees through Higher Levels of SDP Hierarchies
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
Random Structures & Algorithms
On the Approximation Resistance of a Random Predicate
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
3-bit dictator testing: 1 vs. 5/8
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Towards computing the Grothendieck constant
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Polynomial flow-cut gaps and hardness of directed cut problems
Journal of the ACM (JACM)
Drawing (Complete) Binary Tanglegrams
Graph Drawing
Max cut and the smallest eigenvalue
Proceedings of the forty-first annual ACM symposium on Theory of computing
Randomly supported independence and resistance
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conditional hardness for satisfiable 3-CSPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Near-optimal algorithms for maximum constraint satisfaction problems
ACM Transactions on Algorithms (TALG)
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
ACM Transactions on Computation Theory (TOCT)
A better approximation ratio for the vertex cover problem
ACM Transactions on Algorithms (TALG)
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
Approximability Distance in the Space of H-Colourability Problems
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Improved Inapproximability Results for Maximum k-Colorable Subgraph
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Hypergraph Dictatorship Test with Perfect Completeness
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Priority algorithms for graph optimization problems
Theoretical Computer Science
Conditional Hardness of Approximating Satisfiable Max 3CSP-q
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Optimal edge deletions for signed graph balancing
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Vertex cover resists SDPs tightened by local hypermetric inequalities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
FPT algorithms for path-transversals and cycle-transversals problems in graphs
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Conditional hardness of precedence constrained scheduling on identical machines
Proceedings of the forty-second ACM symposium on Theory of computing
Graph expansion and the unique games conjecture
Proceedings of the forty-second ACM symposium on Theory of computing
The UGC Hardness Threshold of the Lp Grothendieck Problem
Mathematics of Operations Research
Untangling the cross-lingual link structure of Wikipedia
ACL '10 Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics
Separator-based data reduction for signed graph balancing
Journal of Combinatorial Optimization
Sharp kernel clustering algorithms and their associated Grothendieck inequalities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast SDP algorithms for constraint satisfaction problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the approximability of the vertex cover and related problems
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
The positive semidefinite Grothendieck problem with rank constraint
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the inapproximability of vertex cover on k-partite k-uniform hypergraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
SDP gaps for 2-to-1 and other label-cover variants
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved inapproximability for submodular maximization
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approximating linear threshold predicates
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
On the conditional hardness of coloring a 4-colorable graph with super-constant number of colors
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approximate Lasserre integrality gap for unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Improved rounding for parallel repeated unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
A query efficient non-adaptive long code test with perfect completeness
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
How to play unique games on expanders
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Unique Games with Entangled Provers Are Easy
SIAM Journal on Computing
Mathematics of Operations Research
Approximability of combinatorial problems with multi-agent submodular cost functions
ACM SIGecom Exchanges
Query-efficient dictatorship testing with perfect completeness
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Directed spanners via flow-based linear programs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On unique games with negativeweights
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Nearly optimal NP-hardness of vertex cover on k-uniform k-partite hypergraphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating the influence of monotone boolean functions in O(√n) query complexity
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the Approximability of Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Strong and weak edges of a graph and linkages with the vertex cover problem
Discrete Applied Mathematics
Approximating edge dominating set in dense graphs
Theoretical Computer Science
Integrality Gaps of $2-o(1)$ for Vertex Cover SDPs in the Lovász-Schrijver Hierarchy
SIAM Journal on Computing
Randomly Supported Independence and Resistance
SIAM Journal on Computing
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
A Counterexample to Strong Parallel Repetition
SIAM Journal on Computing
Beating the Random Ordering Is Hard: Every Ordering CSP Is Approximation Resistant
SIAM Journal on Computing
Hardness of Precedence Constrained Scheduling on Identical Machines
SIAM Journal on Computing
Bounds on locally testable codes with unique tests
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Linear programming, width-1 CSPs, and robust satisfaction
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Linear index coding via semidefinite programming
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the hardness of pricing loss-leaders
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Complexity and approximation of the minimum recombination haplotype configuration problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Subsampling mathematical relaxations and average-case complexity
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds on the approximability of almost-satisfiable Horn SAT and exact hitting set
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Hardness results for agnostically learning low-degree polynomial threshold functions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of finding independent sets in bounded degree (hyper)graphs of low chromatic number
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Better inapproximability results for maxclique, chromatic number and min-3lin-deletion
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Approximating Linear Threshold Predicates
ACM Transactions on Computation Theory (TOCT)
On the approximability and hardness of minimum topic connected overlay and its special instances
Theoretical Computer Science
On 2-query codeword testing with near-perfect completeness
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Approximability of economic equilibrium for housing markets with duplicate houses
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Controlling infection by blocking nodes and links simultaneously
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Approximating vertex cover in dense hypergraphs
Journal of Discrete Algorithms
Solution of the propeller conjecture in R3
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A new point of NP-hardness for unique games
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Hypercontractivity, sum-of-squares proofs, and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for semi-random partitioning problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Robust satisfiability of constraint satisfaction problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Improved parameterized algorithms for above average constraint satisfaction
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized complexity of maxsat above average
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
Minimizing the sum of weighted completion times in a concurrent open shop
Operations Research Letters
An edge-reduction algorithm for the vertex cover problem
Operations Research Letters
FPT algorithms for path-transversal and cycle-transversal problems
Discrete Optimization
A hybridization between memetic algorithm and semidefinite relaxation for the max-cut problem
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Local Versus Global Properties of Metric Spaces
SIAM Journal on Computing
Parallel Repetition in Projection Games and a Concentration Bound
SIAM Journal on Computing
Constraint satisfaction problems parameterized above or below tight bounds: a survey
The Multivariate Algorithmic Revolution and Beyond
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
Maximum edge-cuts in cubic graphs with large girth and in random cubic graphs
Random Structures & Algorithms
Vertex cover in graphs with locally few colors
Information and Computation
Towards an optimal query efficient PCP?
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
A characterization of approximation resistance for even k-partite CSPs
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Single machine scheduling with scenarios
Theoretical Computer Science
Approximating vertex cover using edge-based representations
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
Sparsest cut on quotients of the hypercube
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
On the usefulness of predicates
ACM Transactions on Computation Theory (TOCT)
Optimizing password composition policies
Proceedings of the fourteenth ACM conference on Electronic commerce
Sparsest cut on quotients of the hypercube
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Approximation resistance on satisfiable instances for predicates with few accepting inputs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Majority is stablest: discrete and SoS
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Cones of multipowers and combinatorial optimization problems
Computational Mathematics and Mathematical Physics
Explicit Optimal Hardness via Gaussian Stability Results
ACM Transactions on Computation Theory (TOCT)
New NP-Hardness Results for 3-Coloring and 2-to-1 Label Cover
ACM Transactions on Computation Theory (TOCT)
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
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Complexity of approximating CSP with balance / hard constraints
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Parameterized complexity of MaxSat Above Average
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Column Subset Selection Problem is UG-hard
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A 2-prover game is called unique if the answer of one prover uniquely determines the answer of the second prover and vice versa (we implicitly assume games to be one round games). The value of a 2-prover game is the maximum acceptance probability of the verifier over all the prover strategies. We make the following conjecture regarding the power of unique 2-prover games, which we call the Unique Games Conjecture:(MATH) The Unique Games Conjecture: For arbitrarily small constants $ \ \zeta, \ \delta 0$, there exists a constant $k = k(\zeta,\delta)$ such that it is NP-hard to determine whether a unique 2-prover game with answers from a domain of size $k$ has value at least $1-\zeta$ or at most $\delta$. \medskip.(MATH) We show that a positive resolution of this conjecture would imply the following hardness results:For any $\frac{1}{2} 0$, it is NP-hard to distinguish between the instances of the problem 2-Linear-Equations mod 2 where either there exists an assignment that satisfies $1-\epsilon$ fraction of equations or no assignment can satisfy more than $1-\epsilon^t$ fraction of equations. As a corollary of the above result, it is NP-hard to approximate the Min-2CNF-deletion problem within any constant factor.For the constraint satisfaction problem where every constraint is the predicate Not-all-equal($a,b,c$), $ \ a, b, c \in GF(3) \ $, it is NP-hard to distinguish between the instances where either there exists an assignment that satisfies $1-\epsilon$ fraction of the constraints or no assignment satisfies more than $\frac{8}{9}+\epsilon$ fraction of the constraints for an arbitrarily small constant $\epsilon 0$. We also get a hardness result for a slight variation of approximate coloring of 3-uniform hypergraphs..(MATH) We also show that a variation of the Unique Games Conjecture implies that for arbitrarily small constant $\delta 0$ it is hard to find an independent set of size $\delta n$ in a graph that is guaranteed to have an independent set of size $\Omega(n)$.The main idea in all the above results 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. The uniqueness property plays a crucial role in the analysis of these PCPs.(MATH) In light of such interesting consequences, we think it is an important open problem to prove (or disprove) the Unique Games Conjecture. We also present a semi-definite programming based algorithm for finding reasonable prover strategies for a unique 2-prover game. Given a unique 2-prover game with value $1-\zeta$ and answers from a domain of size $k$, this algorithm finds prover strategies that make the verifier accept with probability $1-O(k^2 \zeta^{1/5} \sqrt{\log (\frac{1}{\zeta})})$. This result shows that the domain size $k = k(\zeta, \delta)$ must be sufficiently large if the Unique Games Conjecture is true.