Tournament ranking with expected profit in polynomial time
SIAM Journal on Discrete Mathematics
On the advantage over a random assignment
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number
Discrete Applied Mathematics
Domination analysis of some heuristics for the traveling salesman problem
Discrete Applied Mathematics
Voting paradoxes and digraphs realizations
Advances in Applied Mathematics
Maximum cuts and judicious partitions in graphs without short cycles
Journal of Combinatorial Theory Series B
Domination analysis of combinatorial optimization problems
Discrete Applied Mathematics
Operations Research Letters
On the advantage over a random assignment
Random Structures & Algorithms
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Domination analysis for minimum multiprocessor scheduling
Discrete Applied Mathematics
Combinatorial dominance guarantees for problems with infeasible solutions
ACM Transactions on Algorithms (TALG)
Explicit construction of a small epsilon-net for linear threshold functions
Proceedings of the forty-first annual ACM symposium on Theory of computing
Solving MAX-r-SAT above a tight lower bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Explicit Construction of a Small $\epsilon$-Net for Linear Threshold Functions
SIAM Journal on Computing
Systems of linear equations over F2 and problems parameterized above average
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Dominance guarantees for above-average solutions
Discrete Optimization
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
Constraint satisfaction problems parameterized above or below tight bounds: a survey
The Multivariate Algorithmic Revolution and Beyond
Communication: Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier width
Discrete Applied Mathematics
Domination analysis of algorithms for bipartite boolean quadratic programs
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Hamilton decompositions of regular expanders: Applications
Journal of Combinatorial Theory Series B
Satisfying more than half of a system of linear equations over GF(2): A multivariate approach
Journal of Computer and System Sciences
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Let P be an optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A, n) is the maximum real q such that the solution x(I) obtained by A for any instance I of P of size n is not worse than at least a fraction q of the feasible solutions of I. We describe a deterministic, polynomial-time algorithm with domination ratio 1 - o(1) for the partition problem, and a deterministic, polynomial-time algoritiun with domination ratio Ω(1) for the MaxCut problem and for some far-reaching extensions of it, including Max-r-Sat, for each fixed r. The techniques combine combinatorial and probabilistic methods with tools from harmonic analysis.