We study cost-sharing mechanisms for several fundamental NP-hard combinatorial optimization problems. A cost-sharing mechanism is a protocol that, given bids for a service, determines which bidders to serve and what prices to charge. The mechanism incurs a subset-dependent cost that is implicitly defined by an instance of a combinatorial optimization problem. Three desirable but mutually incomp...

In the recent development ofwrious models of learning inspired by the PAC learning model (introduced by Valiant) there has been a trend towards models which are as representation independent as possible: We review this development and discuss the advantages of representation independence. Motivated by the research in learning, we propose a framework for studying the combinatorial properties of ...

We study a model of Probably Exactly Correct (PExact) learning that can be viewed either as the Exact model (learning from Equivalence Queries only) relaxed so that counterexamples to equivalence queries are distributionally drawn rather than adversarially chosen or as the Probably Approximately Correct (PAC) model strengthened to require a perfect hypothesis. We also introduce a model of Proba...

We give the first polynomial time prediction strategy for any PAC-learnable class C that probabilistically predicts the target with mistake probability poly(log(t)) t = Õ ( 1 t ) where t is the number of trials. The lower bound for the mistake probability is [HLW94]

Inverse iteration is a standard technique for nding selected eigenvectors associated with eigenvalues which are known approximately. At each step the solution of a linear system of equations is required, which is usually done by factorizing the system matrix. When direct factorization is impractical, iterative methods can be applied for solving the linear systems. Several results about terminat...