Christos H. Papadimitriou

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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)
Renal cell carcinoma is characterized by an accumulation of complex chromosomal alterations during tumor progression. Chromosome 3p deletions are known to occur early in the carcinogenesis, but the nature of subsequent events, their interrelationships, and their sequence is poorly understood, as one usually only obtains a single "view" of the dynamic(More)
Comparative genomic hybridization (CGH) is a laboratory method to measure gains and losses in the copy number of chromosomal regions in tumor cells. It is hypothesized that certain DNA gains and losses are related to cancer progression and that the patterns of these changes are relevant to the clinical consequences of the cancer. It is therefore of interest(More)
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)
Comparative genome hybridization (CGH) is a laboratory method to measure gains and losses of chromosomal regions in tumor cells. It is believed that DNA gains and losses in tumor cells do not occur entirely at random, but partly through some flow of causality. Models that relate tumor progression to the occurrence of DNA gains and losses could be very(More)
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)
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)