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- Elias Koutsoupias, Christos H. Papadimitriou
- Computer Science Review
- 1999

In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model where several agents share a very simple network leads to some… (More)

- Christos H. Papadimitriou, Mihalis Yannakakis
- J. Comput. Syst. Sci.
- 1991

W e define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are classes of optimization problems, and in fact contain several natural, well-studied ones. W e show that problems in these classes can be approximated with some bounded error. Furthermore, we show that a number of common optimization problems are complete for MAXSNP… (More)

- Christos H. Papadimitriou, John N. Tsitsiklis
- Math. Oper. Res.
- 1987

- Christos H. Papadimitriou
- J. Comput. Syst. Sci.
- 1994

We define several new complexity classes of search problems, "between" the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph. The… (More)

- Constantinos Daskalakis, Paul W. Goldberg, Christos H. Papadimitriou
- Commun. ACM
- 2005

We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomial time solvability of normal form games and graphical games, establishing that… (More)

Latent semantic indexing (LX) is an information retrieval technique based on the spectral analysis of the term-document matrix, whose empirical success had heretofort been without rigorous prediction and explanation. We prove that, under certain conditions, LSI does succeed in capturing the underlying semantics of the corpus and achieves improved retrieval… (More)

- Elias Dahlhaus, David S. Johnson, Christos H. Papadimitriou, Paul D. Seymour, Mihalis Yannakakis
- SIAM J. Comput.
- 1994

In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. We show that the problem… (More)

We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that… (More)