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Abstract: We investigate the computational complexity of two closely related classes of combinatorial optimization problems for linear systems which arise in various fields such as machine learning, operations research and pattern recognition. In the first class (Min ULR) one wishes, given a possibly infeasible system of linear relations, to find a solution that violates as few relations as possible while satisfying all the others. In the second class (Min RVLS) the linear system is supposed to be... (Update)
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BibTeX entry: (Update)
E. Amaldi and V. Kann. On the approximability of minimizing nonzero variables and unsatisfied relations in linear systems. Theoretical Computer Science, 1997. To appear. Preliminary version available as ECCC Technical Report 96-15. http://citeseer.ist.psu.edu/amaldi97approximability.html More
@article{ amaldi98approximability,
author = "Edoardo Amaldi and Viggo Kann",
title = "On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems",
journal = "Theoretical Computer Science",
volume = "209",
number = "1--2",
pages = "237--260",
year = "1998",
url = "citeseer.ist.psu.edu/amaldi97approximability.html" }
Citations (may not include all citations):4212 Computers and Intractability: a guide to the theory of NP-co.. (context) - Garey, Johnson - 1979
2133 Pattern classification and scene analysis (context) - Duda, Hart - 1973
493 Communications of ACM (context) - Valiant, of et al. - 1984
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248 An introduction to Computational Learning Theory (context) - Kearns, Vazirani - 1994
226 for approximating set cover (context) - Feige, of - 1996
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190 Inductive inference: theory and methods (context) - Angluin, Smith - 1983
184 Cryptographic limitations on learning boolean formulae and f.. - Kearns, Valiant - 1994
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120 The hardness of approximate optima in lattices (context) - Arora, Babai et al. - 1993
120 The hardness of approximate optima in lattices (context) - Arora, Babai et al. - 1997
120 Some optimal inapproximability results (context) - Hastad - 1997
115 PCPs and non-approximability -- towards tight results (context) - Bellare, Goldreich et al. - 1995
106 Discriminant analysis and statistical pattern recognition (context) - McLachlan - 1992
95 Fundamentals of artificial neural networks (context) - Hassoun - 1995
77 Perceptron-based learning algorithms (context) - Gallant - 1990
51 the Approximability of NP-complete Optimization Problems (context) - Kann - 1992
48 The complexity and approximability of finding maximum feasib.. - Amaldi, Kann - 1995
47 Constraint satisfaction: the approximability of minimization.. - Khanna, Sudan et al. - 1997
47 Clique is hard to approximate within n 1\Gammaffl (context) - Hastad - 1996
45 Approximating minimum feedback sets and multi-cuts in direct.. - Even, Naor et al. - 1995
42 Packing directed circuits fractionally (context) - Seymour - 1995
42 Algorithms and Complexity (context) - Papadimitriou, Steiglitz - 1982
41 Completeness in approximation classes (context) - Crescenzi, Panconesi - 1991
37 Structure in approximation classes - Crescenzi, Kann et al. - 1995
37 To weight or not to weight: Where is the question - Crescenzi, Silvestri et al. - 1996
36 La Sapienza (context) - Crescenzi, Kann et al. - 1995
30 Robust trainability of single neurons - Hoffgen, Simon et al. - 1995
29 Complexity results on learning by neural nets - Lin, Vitter - 1991
26 Misclassification minimization - Mangasarian - 1994
24 Freeman and Co (context) - Chvatal - 1983
20 Polynomially bounded minimization problems that are hard to .. - Kann - 1994
19 A thermal perceptron learning rule (context) - Frean - 1992
18 On learning simple neural concepts: from halfspace intersect.. - Marchand, Golea - 1993
18 the complexity of training perceptrons (context) - Amaldi - 1991
15 Theoretical Computer Science (context) - Johnson, Preparata et al. - 1978
14 Locating minimal infeasible constraint sets in linear progra.. (context) - Chinneck, Dravnieks - 1991
14 From finding maximum feasible subsystems of linear systems t.. (context) - Amaldi - 1994
12 Approximating the minimum maximal independence number (context) - Halld'orsson - 1993
11 The minimum feature set problem (context) - van Horn, Martinez - 1992
11 The minimum feature set problem (context) - van Horn, Martinez - 1994
10 Interscience series in discrete mathematics and optimization (context) - Schrijver, linear et al. - 1986
10 Identifying minimally infeasible subsystems of inequalities (context) - Gleeson, Ryan - 1990
8 Linear discriminant functions determined by genetic search (context) - Koehler - 1991
7 Strong lower bounds on the approximability of some NPO PB-co.. - Kann - 1995
7 Trees and Hills: Methodology for Maximizing Functions of Sys.. (context) - Greer - 1984
7 Approaches to diagnosing infeasible linear programs (context) - Greenberg, Murphy - 1991
7 Minimizing misclassifications in linear discriminant analysi.. (context) - Koehler, Erenguc - 1990
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6 An algorithm for optimal solution of linear inequalities and.. (context) - Warmack, Gonzalez - 1973
6 An effective polynomial-time heuristic for the minimum-cardi.. (context) - Chinneck - 1996
6 Finding the minimum weight IIS cover of an infeasible system.. (context) - Parker, Ryan - 1996
5 A note on resolving infeasibility in linear programs by cons.. (context) - Sankaran - 1993
5 A set covering approach to infeasibility analysis of linear .. - Parker - 1995
3 Complexity of problems related to training perceptrons (context) - Amaldi - 1992
3 Hardness of approximation (context) - Kann, Panconesi - 1997
3 Redundency and Helly for linear programming (context) - Edmonds - 1994
2 Analyzing infeasible mixed-integer and integer linear progra.. (context) - Guieu, Chinneck - 1996
2 the difficulty of designing good classifiers - Grigni, Mirelli et al. - 1996
1 Annals of Mathematics and Artificial Intelligence (context) - Greenberg, redundancy et al. - 1996
1 Feasibility and viability (context) - Chinneck - 1997
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