On the Approximability of Minimizing Nonzero Variables or Unsatisfied Relations in Linear Systems

[1]  Lars Engebretsen,et al.  Clique Is Hard To Approximate Within , 2000 .

[2]  J. Håstad Clique is hard to approximate withinn1−ε , 1999 .

[3]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[4]  John W. Chinneck,et al.  Analyzing Infeasible Mixed-Integer and Integer Linear Programs , 1999, INFORMS J. Comput..

[5]  John M. Wilson,et al.  Advances in Sensitivity Analysis and Parametric Programming , 1998, J. Oper. Res. Soc..

[6]  U. Feige A threshold of ln n for approximating set cover , 1998, JACM.

[7]  Mauro Dell'Amico,et al.  Annotated Bibliographies in Combinatorial Optimization , 1997 .

[8]  Luca Trevisan,et al.  Constraint satisfaction: the approximability of minimization problems , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[9]  Johan Håstad,et al.  Some optimal inapproximability results , 1997, STOC '97.

[10]  John W. Chinneck,et al.  Feasibility and Viability , 1997 .

[11]  Luca Trevisan,et al.  Structure in Approximation Classes , 1999, Electron. Colloquium Comput. Complex..

[12]  Christos H. Papadimitriou,et al.  On the Difficulty of Designing Good Classifiers , 1996, SIAM J. Comput..

[13]  M.H. Hassoun,et al.  Fundamentals of Artificial Neural Networks , 1996, Proceedings of the IEEE.

[14]  Luca Trevisan,et al.  To Weight or Not to Weight: Where is the Question? , 1996, ISTCS.

[15]  Bruce A. Reed,et al.  Packing directed circuits , 1996, Comb..

[16]  Mihir Bellare,et al.  Free bits, PCPs and non-approximability-towards tight results , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[17]  Viggo Kann,et al.  Strong Lower Bounds on the Approximability of some NPO PB-Complete Maximization Problems , 1995, MFCS.

[18]  Edoardo Amaldi,et al.  The Complexity and Approximability of Finding Maximum Feasible Subsystems of Linear Relations , 1995, Theor. Comput. Sci..

[19]  Paul D. Seymour,et al.  Packing directed circuits fractionally , 1995, Comb..

[20]  Joseph Naor,et al.  Approximating Minimum Feedback Sets and Multi-Cuts in Directed Graphs , 1995, IPCO.

[21]  E. Amaldi,et al.  On the Approximability of Removing the Smallest Number of Relations from Linear Systems to Achieve Feasibility , 1995 .

[22]  Richard LundgrenBurt SimonDate A Set Covering Approach to Infeasibility Analysis of Linear Programming Problems and Related Issues By , 1995 .

[23]  Carsten Lund,et al.  On the hardness of approximating minimization problems , 1994, JACM.

[24]  Tony R. Martinez,et al.  The minimum feature set problem , 1994, Neural Networks.

[25]  Leslie G. Valiant,et al.  Cryptographic limitations on learning Boolean formulae and finite automata , 1994, JACM.

[26]  Viggo Kann,et al.  Polynomially Bounded Minimization Problems That Are Hard to Approximate , 1993, Nord. J. Comput..

[27]  Umesh V. Vazirani,et al.  An Introduction to Computational Learning Theory , 1994 .

[28]  Edoardo Amaldi,et al.  From finding maximum feasible subsystems of linear systems to feedforward neural network design , 1994 .

[29]  MinimizationO. L. Mangasarian Misclassiication Minimization , 1994 .

[30]  Pierluigi Crescenzi,et al.  A compendium of NP optimization problems , 1994, WWW Spring 1994.

[31]  Carsten Lund,et al.  Efficient probabilistically checkable proofs and applications to approximations , 1993, STOC.

[32]  Magnús M. Halldórsson,et al.  Approximating the Minimum Maximal Independence Number , 1993, Inf. Process. Lett..

[33]  Jayaram K. Sankaran A note on resolving infeasibility in linear programs by constraint relaxation , 1993, Oper. Res. Lett..

[34]  Jacques Stern,et al.  The hardness of approximate optima in lattices, codes, and systems of linear equations , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[35]  Mario Marchand,et al.  On learning simple neural concepts: from halfspace intersections to neural decision lists , 1993 .

[36]  Marcus R. Frean,et al.  A "Thermal" Perceptron Learning Rule , 1992, Neural Computation.

[37]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[38]  Hans Ulrich Simon,et al.  Robust Trainability of Single Neurons , 1995, J. Comput. Syst. Sci..

[39]  G. McLachlan Discriminant Analysis and Statistical Pattern Recognition , 1992 .

[40]  O. Mangasarian,et al.  Robust linear programming discrimination of two linearly inseparable sets , 1992 .

[41]  Gary J. Koehler,et al.  Linear Discriminant Functions Determined by Genetic Search , 1991, INFORMS J. Comput..

[42]  Harvey J. Greenberg,et al.  Approaches to Diagnosing Infeasible Linear Programs , 1991, INFORMS J. Comput..

[43]  John W. Chinneck,et al.  Locating Minimal Infeasible Constraint Sets in Linear Programs , 1991, INFORMS J. Comput..

[44]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity , 1994 .

[45]  Stephen I. Gallant,et al.  Perceptron-based learning algorithms , 1990, IEEE Trans. Neural Networks.

[46]  Jennifer Ryan,et al.  Identifying Minimally Infeasible Subsystems of Inequalities , 1990, INFORMS J. Comput..

[47]  Gary J. Koehler,et al.  Minimizing Misclassifications in Linear Discriminant Analysis , 1990 .

[48]  H. P. Williams THEORY OF LINEAR AND INTEGER PROGRAMMING (Wiley-Interscience Series in Discrete Mathematics and Optimization) , 1989 .

[49]  Alessandro Panconesi,et al.  Completeness in Approximation Classes , 1989, Inf. Comput..

[50]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[51]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[52]  R. Greer Trees and Hills: Methodology for Maximizing Functions of Systems of Linear Relations , 1984 .

[53]  Carl H. Smith,et al.  Inductive Inference: Theory and Methods , 1983, CSUR.

[54]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[55]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[56]  Franco P. Preparata,et al.  The Densest Hemisphere Problem , 1978, Theor. Comput. Sci..

[57]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[58]  R. E. Warmack,et al.  An Algorithm for the Optimal Solution of Linear Inequalities and its Application to Pattern Recognition , 1973, IEEE Transactions on Computers.

[59]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .