Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
New local search approximation techniques for maximum generalized satisfiability problems
CIAC '94 Proceedings of the second Italian conference on Algorithms and complexity
New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Approximation algorithms
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The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
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(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Designing networks with good equilibria
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On Satisfiability Games and the Power of Congestion Games
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the performance of congestion games for optimum satisfiability problems
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Total latency in singleton congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Weighted Boolean formula games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Exact price of anarchy for polynomial congestion games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Coordination mechanisms for selfish scheduling
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Operations Research
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We propose approximation algorithms under game-theoretic considerations. We indroduce and study the general covering problem which is a natural generalization of the well-studied max-n -cover problem. In the general covering problem, we are given a universal set of weighted elements E and n collections of subsets of the elements. The task is to choose one subset from each collection such that the total weight of their union is as large as possible. In our game-theoretic setting, the choice in each collection is made by an independent player. For covering an element, the players receive a payoff defined by a non-increasing utility sharing function. This function defines the fraction that each covering player receives from the weight of the elements. We show how to construct a utility sharing function such that every Nash Equilibrium approximates the optimal solution by a factor of $1-{{1} \over {e}}$. We also prove that any sequence of unilateral improving steps is polynomially bounded. This gives rise to a polynomial-time local search approximation algorithm whose approximation ratio is best possible.