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We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class <b>PPAD</b> (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building upon the work of Daskalakis et al. [2006a] on the complexity of four-player Nash equilibria, settles a long standing(More)
Even though many people thought the problem of finding Nash equilibria is hard in general, and it has been proven so for games among three or more players recently, it's not clear whether the two-player case can be shown in the same class of PPAD-complete problems. We prove that the problem of finding a Nash equilibrium in a two-player game is PPAD-complete
In this paper, we propose a phrase-based document similarity to compute the pair-wise similarities of documents based on the suffix tree document (STD) model. By mapping each node in the suffix tree of STD model into a unique feature term in the vector space document (VSD) model, the phrase-based document similarity naturally inherits the term tf-idf(More)
The authors advance significantly beyond the recent progress on the algorithmic complexity of Nash equilibria by solving two major open problems in the approximation of Nash equilibria and in the smoothed analysis of algorithms. (1) The authors show that no algorithm with complexity poly(n, 1/epsi) can compute an epsi-approximate Nash equilibrium in a(More)
We are interested in the problem of word extraction from Chinese text collections. We define a word to be a meaningful string composed of several Chinese characters. For example, , 'percent', and , 'more and more', are not recognized as traditional Chinese words from the viewpoint of some people. However, in our work, they are words because they are very(More)
A multiprocessor system is unlikely to have access to information about the execution characteristics of the jobs it is to schedule. In this work, we are interested in scheduling algorithms for batch jobs that require no such knowledge (such algorithms are called non-clairvoyant). Preemptive scheduling (i.e., redistribution of processors) is important to(More)