@article{MR2032567, AUTHOR = {Dinur, Irit and Safra, Shmuel}, TITLE = {On the hardness of approximating label-cover}, JOURNAL = {Inform. Process. Lett.}, FJOURNAL = {Information Processing Letters}, VOLUME = {89}, YEAR = {2004}, NUMBER = {5}, PAGES = {247--254}, ISSN = {0020-0190}, CODEN = {IFPLAT}, MRCLASS = {68Q15 (05C78 68Q17 68Q25)}, MRNUMBER = {2 032 567}, } @inproceedings{MR2004a:68163, AUTHOR = {Feige, Uriel}, TITLE = {Approximation thresholds for combinatorial optimization problems}, BOOKTITLE = {Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002)}, PAGES = {649--658}, PUBLISHER = {Higher Ed. Press}, ADDRESS = {Beijing}, YEAR = {2002}, MRCLASS = {68W25 (68Q17)}, MRNUMBER = {2004a:68163}, } @article{MR99k:68076, AUTHOR = {Feige, Uriel and Kilian, Joe}, TITLE = {Zero knowledge and the chromatic number}, NOTE = {Complexity 96---The Eleventh Annual IEEE Conference on Computational Complexity (Philadelphia, PA)}, JOURNAL = {J. Comput. System Sci.}, FJOURNAL = {Journal of Computer and System Sciences}, VOLUME = {57}, YEAR = {1998}, NUMBER = {2}, PAGES = {187--199}, ISSN = {0022-0000}, CODEN = {JCSSBM}, MRCLASS = {68Q25 (05C15 68Q15 68R10)}, MRNUMBER = {99k:68076}, } @book{MR2001f:68002, AUTHOR = {Ausiello, G. and Crescenzi, P. and Gambosi, G. and Kann, V. and Marchetti-Spaccamela, A. and Protasi, M.}, TITLE = {Complexity and approximation}, NOTE = {Combinatorial optimization problems and their approximability properties, With 1 CD-ROM (Windows and UNIX)}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1999}, PAGES = {xx+524}, ISBN = {3-540-65431-3}, MRCLASS = {68-02 (65Y20 90-01 90C27 90C60)}, MRNUMBER = {2001f:68002}, MRREVIEWER = {Alexander I. Barvinok}, } @misc{compendium, author = {Pierluigi Crescenzi and Viggo Kann (eds.)}, title = {A Compendium of {NP}-optimization Problems}, note = {http://www.nada.kth.se/%7Eviggo/problemlist/}, } @article{MR84a:90044, AUTHOR = {Gr{\"o}tschel, M. and Lov{\'a}sz, L. and Schrijver, A.}, TITLE = {The ellipsoid method and its consequences in combinatorial optimization}, JOURNAL = {Combinatorica}, FJOURNAL = {Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society}, VOLUME = {1}, YEAR = {1981}, NUMBER = {2}, PAGES = {169--197}, ISSN = {0209-9683}, CODEN = {COMBDI}, MRCLASS = {90C05 (05Cxx)}, MRNUMBER = {84a:90044}, } @article{fourier1826a, AUTHOR = {Fourier, J. B. J.}, TITLE = {Solution d'une question particuli\`ere du calcul des in\'egalit\'es}, JOURNAL = {Nouveau Bulletin des Sciences par la Soci\'et\'e philomathique de Paris}, YEAR = {1826}, PAGES = {99--100}, } @article{MR18:417d, AUTHOR = {Kuhn, H. W.}, TITLE = {Solvability and consistency for linear equations and inequalities}, JOURNAL = {Amer. Math. Monthly}, VOLUME = {63}, YEAR = {1956}, PAGES = {217--232}, } @article{MR95k:90066, AUTHOR = {Goemans, Michel X. and Williamson, David P.}, TITLE = {A general approximation technique for constrained forest problems}, JOURNAL = {SIAM J. Comput.}, FJOURNAL = {SIAM Journal on Computing}, VOLUME = {24}, YEAR = {1995}, NUMBER = {2}, PAGES = {296--317}, ISSN = {0097-5397}, CODEN = {SMJCAT}, MRCLASS = {90C27 (68Q25 68R10)}, MRNUMBER = {95k:90066}, MRREVIEWER = {Olivia M. Carducci}, } @article {MR96c:68146, AUTHOR = {Agrawal, Ajit and Klein, Philip and Ravi, R.}, TITLE = {When trees collide: an approximation algorithm for the generalized {S}teiner problem on networks}, JOURNAL = {SIAM J. Comput.}, FJOURNAL = {SIAM Journal on Computing}, VOLUME = {24}, YEAR = {1995}, NUMBER = {3}, PAGES = {440--456}, ISSN = {0097-5397}, CODEN = {SMJCAT}, MRCLASS = {68R10 (68M10 68Q20)}, MRNUMBER = {96c:68146}, } @incollection{goemans-williamson-primal-dual, AUTHOR = {Michael X. Goemans and David Williamson}, TITLE = {The Primal-Dual Method for Approximation Algorithms and its Application to Network Design Problems}, BOOKTITLE = {Approximation Algorithms for NP-Hard Problems}, EDITOR = {Dorit Hochbaum}, PAGES = {144--191}, PUBLISHER = {PWS Publishing Company}, YEAR = {1997}, } @article{MR84a:90052, AUTHOR = {Bar-Yehuda, R. and Even, S.}, TITLE = {A linear-time approximation algorithm for the weighted vertex cover problem}, JOURNAL = {J. Algorithms}, FJOURNAL = {Journal of Algorithms}, VOLUME = {2}, YEAR = {1981}, NUMBER = {2}, PAGES = {198--203}, ISSN = {0196-6774}, CODEN = {JOALDV}, MRCLASS = {90C10 (05C70 52A37 68C25)}, MRNUMBER = {84a:90052}, MRREVIEWER = {Klaus Lommatzsch}, } @inproceedings{MR1427527, AUTHOR = {Feige, Uriel}, TITLE = {A threshold of {$\ln n$} for approximating set cover (preliminary version)}, BOOKTITLE = {Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing (Philadelphia, PA, 1996)}, PAGES = {314--318}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {1996}, MRCLASS = {68Q25 (68Q15)}, MRNUMBER = {1 427 527}, } @article{MR19:379d, AUTHOR = {Ryser, H. J.}, TITLE = {Combinatorial properties of matrices of zeros and ones}, JOURNAL = {Canad. J. Math.}, VOLUME = {9}, YEAR = {1957}, PAGES = {371--377}, MRCLASS = {05.0X}, MRNUMBER = {19,379d}, MRREVIEWER = {Marshall Hall, Jr.}, } @article{MR18:267a, AUTHOR = {Orden, Alex}, TITLE = {The transhipment problem}, JOURNAL = {Management Sci.}, VOLUME = {2}, YEAR = {1956}, PAGES = {276--285}, MRCLASS = {90.0X}, MRNUMBER = {18,267a}, MRREVIEWER = {K. J. Arrow}, } @incollection{MR15:48b, AUTHOR = {Dantzig, George B.}, TITLE = {Application of the simplex method to a transportation problem}, BOOKTITLE = {Activity Analysis of Production and Allocation}, SERIES = {Cowles Commission Monograph No. 13}, PAGES = {359--373}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York, N. Y.}, YEAR = {1951}, MRCLASS = {90.0X}, MRNUMBER = {15,48b}, MRREVIEWER = {H. W. Kuhn}, } @article{MR19:1024a, AUTHOR = {Gale, David}, TITLE = {A theorem on flows in networks}, JOURNAL = {Pacific J. Math.}, VOLUME = {7}, YEAR = {1957}, PAGES = {1073--1082}, MRCLASS = {90.0X}, MRNUMBER = {19,1024a}, MRREVIEWER = {P. Wolfe}, } @article{MR57:2505, AUTHOR = {Cunningham, W. H.}, TITLE = {A network simplex method}, JOURNAL = {Math. Programming}, VOLUME = {11}, YEAR = {1976}, NUMBER = {2}, PAGES = {105--116}, MRCLASS = {90B10 (90C35)}, MRNUMBER = {57 \#2505}, MRREVIEWER = {Der-San Chen}, } @article{MR91g:68069, AUTHOR = {Alon, Noga}, TITLE = {Generating pseudo-random permutations and maximum flow algorithms}, JOURNAL = {Inform. Process. Lett.}, FJOURNAL = {Information Processing Letters}, VOLUME = {35}, YEAR = {1990}, NUMBER = {4}, PAGES = {201--204}, ISSN = {0020-0190}, CODEN = {IFPLAT}, MRCLASS = {68Q25 (05A05 68R05)}, MRNUMBER = {91g:68069}, } @incollection{MR1076825, AUTHOR = {Cheriyan, Joseph and Hagerup, Torben and Mehlhorn, Kurt}, TITLE = {Can a maximum flow be computed in {$o(nm)$} time?}, BOOKTITLE = {Automata, languages and programming (Coventry, 1990)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {443}, PAGES = {235--248}, PUBLISHER = {Springer}, ADDRESS = {New York}, YEAR = {1990}, MRCLASS = {68Q25 (90B10)}, MRNUMBER = {1 076 825}, } @article{MR92e:68063, AUTHOR = {Ahuja, Ravindra K. and Mehlhorn, Kurt and Orlin, James B. and Tarjan, Robert E.}, TITLE = {Faster algorithms for the shortest path problem}, JOURNAL = {J. Assoc. Comput. Mach.}, FJOURNAL = {Journal of the Association for Computing Machinery}, VOLUME = {37}, YEAR = {1990}, NUMBER = {2}, PAGES = {213--223}, ISSN = {0004-5411}, CODEN = {JACOAH}, MRCLASS = {68Q25 (05C35 68R10 90B10)}, MRNUMBER = {92e:68063}, } @article{MR91d:68046, AUTHOR = {Ahuja, Ravindra K. and Orlin, James B. and Tarjan, Robert E.}, TITLE = {Improved time bounds for the maximum flow problem}, JOURNAL = {SIAM J. Comput.}, FJOURNAL = {SIAM Journal on Computing}, VOLUME = {18}, YEAR = {1989}, NUMBER = {5}, PAGES = {939--954}, ISSN = {0097-5397}, CODEN = {SMJCAT}, MRCLASS = {68Q25 (90B10)}, MRNUMBER = {91d:68046}, } @incollection{MR92i:90043, AUTHOR = {Goldberg, Andrew V. and Tardos, {\'E}va and Tarjan, Robert E.}, TITLE = {Network flow algorithms}, BOOKTITLE = {Paths, flows, and VLSI-layout (Bonn, 1988)}, SERIES = {Algorithms Combin.}, VOLUME = {9}, PAGES = {101--164}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1990}, MRCLASS = {90B10 (68Q25 68R10)}, MRNUMBER = {92i:90043}, MRREVIEWER = {Ondrej S{\'y}kora}, } @article{MR92c:90050, AUTHOR = {Goldberg, Andrew V. and Tarjan, Robert E.}, TITLE = {A new approach to the maximum-flow problem}, JOURNAL = {J. Assoc. Comput. Mach.}, FJOURNAL = {Journal of the Association for Computing Machinery}, VOLUME = {35}, YEAR = {1988}, NUMBER = {4}, PAGES = {921--940}, ISSN = {0004-5411}, CODEN = {JACOAH}, MRCLASS = {90B10 (68Q25)}, MRNUMBER = {92c:90050}, MRREVIEWER = {Robert E. Beck}, } @article {MR91m:90058, AUTHOR = {Goldberg, Andrew V. and Tarjan, Robert E.}, TITLE = {Finding minimum-cost circulations by canceling negative cycles}, JOURNAL = {J. Assoc. Comput. Mach.}, FJOURNAL = {Journal of the Association for Computing Machinery}, VOLUME = {36}, YEAR = {1989}, NUMBER = {4}, PAGES = {873--886}, ISSN = {0004-5411}, CODEN = {JACOAH}, MRCLASS = {90B10}, MRNUMBER = {91m:90058}, MRREVIEWER = {Claude Benzaken}, } @article {MR91f:68085, AUTHOR = {Goldberg, Andrew V. and Tarjan, Robert E.}, TITLE = {A parallel algorithm for finding a blocking flow in an acyclic network}, JOURNAL = {Inform. Process. Lett.}, FJOURNAL = {Information Processing Letters}, VOLUME = {31}, YEAR = {1989}, NUMBER = {5}, PAGES = {265--271}, ISSN = {0020-0190}, CODEN = {IFPLAT}, MRCLASS = {68Q25 (68Q22 68R10 90B10)}, MRNUMBER = {91f:68085}, } @article {MR91d:90038, AUTHOR = {Goldberg, Andrew V. and Tarjan, Robert E.}, TITLE = {Finding minimum-cost circulations by successive approximation}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {15}, YEAR = {1990}, NUMBER = {3}, PAGES = {430--466}, ISSN = {0364-765X}, MRCLASS = {90B10}, MRNUMBER = {91d:90038}, } @TechReport{goldberg1985, author = {Andrew V. Goldberg}, title = {A new max-flow algorithm}, institution = {Laboratory for Computer Science, MIT}, number = {MIT/LCS/TM-291}, address = {Cambridge}, year = {1985}, } @article{MR44:5178, AUTHOR = {Dinic, E. A.}, TITLE = {An algorithm for the solution of the problem of maximal flow in a network with power estimation}, JOURNAL = {Dokl. Akad. Nauk SSSR}, VOLUME = {194}, YEAR = {1970}, PAGES = {754--757}, MRCLASS = {94.30}, MRNUMBER = {44 \#5178}, MRREVIEWER = {P. Vondr{\'a}{\v{c}}ek}, } @article{MR49:8619, AUTHOR = {Karzanov, A. V.}, TITLE = {The problem of finding the maximal flow in a network by the method of preflows}, JOURNAL = {Dokl. Akad. Nauk SSSR}, VOLUME = {215}, YEAR = {1974}, PAGES = {49--52}, MRCLASS = {90B10}, MRNUMBER = {49 \#8619}, MRREVIEWER = {M. Manas}, } @incollection{MR42:1583, AUTHOR = {Edmonds, Jack and Karp, Richard M.}, TITLE = {Theoretical improvements in algorithmic efficiency for network flow problems}, BOOKTITLE = {Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969)}, PAGES = {93--96}, PUBLISHER = {Gordon and Breach}, ADDRESS = {New York}, YEAR = {1970}, MRCLASS = {94.30}, MRNUMBER = {42 \#1583}, MRREVIEWER = {D. R. Fulkerson}, } @incollection{MR19:719c, AUTHOR = {Dantzig, G. B. and Ford, Jr., L. R. and Fulkerson, D. R.}, TITLE = {A primal-dual algorithm for linear programs}, BOOKTITLE = {Linear inequalities and related systems}, SERIES = {Annals of Mathematics Studies, no. 38}, PAGES = {171--181}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, N. J.}, YEAR = {1956}, MRCLASS = {90.0X}, MRNUMBER = {19,719c}, MRREVIEWER = {P. S. Dwyer}, } @article{MR17:759d, AUTHOR = {Kuhn, H. W.}, TITLE = {The {H}ungarian method for the assignment problem}, JOURNAL = {Naval Res. Logist. Quart.}, VOLUME = {2}, YEAR = {1955}, PAGES = {83--97}, MRCLASS = {90.0X}, MRNUMBER = {17,759d}, MRREVIEWER = {D. Gale}, } @article{kotzig-1956, AUTHOR = {A. Kotzig}, TITLE = {S\'uvislost' a Pravidelin\'a S\'uvislost' Kone\v{c}n\'ych Grafov}, JOURNAL = {Bratislava: Vysok\'a \v{S}kola Ekonomick\'a}, YEAR = {1956}, } @article{elias-1956, AUTHOR = {P. Elias and A. Feinstein and C. E. Shannon}, TITLE = {Note on maximal flow through a network}, JOURNAL = {IRE Transactions on Information Theory IT-2}, YEAR = {1956}, PAGES = {117--199}, } @article{MR18:56h, AUTHOR = {Ford, Jr., L. R. and Fulkerson, D. R.}, TITLE = {Maximal flow through a network}, JOURNAL = {Canad. J. Math.}, VOLUME = {8}, YEAR = {1956}, PAGES = {399--404}, } @article{MR87i:90162, AUTHOR = {Hall, Nicholas G. and Hochbaum, Dorit S.}, TITLE = {A fast approximation algorithm for the multicovering problem}, JOURNAL = {Discrete Appl. Math.}, FJOURNAL = {Discrete Applied Mathematics. Combinatorial Algorithms, Optimization and Computer Science}, VOLUME = {15}, YEAR = {1986}, NUMBER = {1}, PAGES = {35--40}, ISSN = {0166-218X}, CODEN = {DAMADU}, MRCLASS = {90C10}, MRNUMBER = {87i:90162}, } @article{MR56:7317, AUTHOR = {Johnson, David S.}, TITLE = {Approximation algorithms for combinatorial problems}, NOTE = {Fifth Annual ACM Symposium on the Theory of Computing (Austin, Tex., 1973)}, JOURNAL = {J. Comput. System Sci.}, VOLUME = {9}, YEAR = {1974}, PAGES = {256--278}, MRCLASS = {68A20 (65K05)}, MRNUMBER = {56 \#7317}, MRREVIEWER = {A. V. Anisimov}, } @article{MR52:5452, AUTHOR = {Lov{\'a}sz, L.}, TITLE = {On the ratio of optimal integral and fractional covers}, JOURNAL = {Discrete Math.}, VOLUME = {13}, YEAR = {1975}, NUMBER = {4}, PAGES = {383--390}, MRCLASS = {05B40}, MRNUMBER = {52 \#5452}, MRREVIEWER = {Torrence D. Parsons}, } @article{MR83g:90089, AUTHOR = {Hochbaum, Dorit S.}, TITLE = {Approximation algorithms for the set covering and vertex cover problems}, JOURNAL = {SIAM J. Comput.}, FJOURNAL = {SIAM Journal on Computing}, VOLUME = {11}, YEAR = {1982}, NUMBER = {3}, PAGES = {555--556}, ISSN = {0097-5397}, CODEN = {SMJCAT}, MRCLASS = {90C10 (65K05)}, MRNUMBER = {83g:90089}, } @inProceedings{garey-graham-ullman, AUTHOR = {M. R. Garey and R. L. Graham and J. D. Ullman}, TITLE = {Worst Case Analysis of Memory Allocation Algorithms}, BOOKTITLE = {Proceedings of the Fourth Annual ACM Symposium on Theory of Computing (STOC)}, PAGES = {143--150}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {1972}, } @incollection{MR54:9659, AUTHOR = {Garey, M. R. and Graham, R. L. and Ullman, J. D.}, TITLE = {An analysis of some packing algorithms}, BOOKTITLE = {Combinatorial algorithms (Courant Comput. Sci. Sympos., No. 9, 1972)}, PAGES = {39--47}, PUBLISHER = {Algorithmics Press, New York}, YEAR = {1973}, } @book{MR2002h:68001, AUTHOR = {Vazirani, Vijay V.}, TITLE = {Approximation algorithms}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2001}, PAGES = {xx+378}, ISBN = {3-540-65367-8}, MRCLASS = {68-02 (68Q17 68Q25 68W25 90Cxx)}, MRNUMBER = {2002h:68001}, MRREVIEWER = {Mark R. Jerrum}, } @book{MR99f:90002, AUTHOR = {Wolsey, Laurence A.}, TITLE = {Integer programming}, SERIES = {Wiley-Interscience Series in Discrete Mathematics and Optimization}, NOTE = {A Wiley-Interscience Publication}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York}, YEAR = {1998}, PAGES = {xx+264}, ISBN = {0-471-28366-5}, MRCLASS = {90-01 (90C10)}, MRNUMBER = {99f:90002}, MRREVIEWER = {Anton Volgenant}, } @inProceedings{spielman-teng-2001, AUTHOR = {Spielman, Daniel A. and Teng, Shang-Hua}, TITLE = {Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time}, BOOKTITLE = {Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing (STOC'2001, Heraklion, Crete, Greece)}, PAGES = {296--305}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {2001}, } @article{MR92h:52017, AUTHOR = {Kalai, Gil and Kleitman, Daniel J.}, TITLE = {A quasi-polynomial bound for the diameter of graphs of polyhedra}, JOURNAL = {Bull. Amer. Math. Soc. (N.S.)}, FJOURNAL = {American Mathematical Society. Bulletin. New Series}, VOLUME = {26}, YEAR = {1992}, NUMBER = {2}, PAGES = {315--316}, ISSN = {0273-0979}, CODEN = {BAMOAD}, MRCLASS = {52B55}, MRNUMBER = {92h:52017}, MRREVIEWER = {W. J. Firey}, } @article{MR51:7611, AUTHOR = {Jeroslow, R. G.}, TITLE = {The simplex algorithm with the pivot rule of maximizing criterion improvement}, JOURNAL = {Discrete Math.}, VOLUME = {4}, YEAR = {1973}, PAGES = {367--377}, MRCLASS = {90C05}, MRNUMBER = {51 \#7611}, MRREVIEWER = {S. Cruceanu}, } @article{MR57:5793, AUTHOR = {Bland, Robert G.}, TITLE = {A combinatorial abstraction of linear programming}, JOURNAL = {J. Combinatorial Theory Ser. B}, VOLUME = {23}, YEAR = {1977}, NUMBER = {1}, PAGES = {33--57}, MRCLASS = {05B35 (90C05)}, MRNUMBER = {57 \#5793}, MRREVIEWER = {Andras Recski}, } @article{MR56:17791, AUTHOR = {Bland, Robert G.}, TITLE = {New finite pivoting rules for the simplex method}, JOURNAL = {Math. Oper. Res.}, VOLUME = {2}, YEAR = {1977}, NUMBER = {2}, PAGES = {103--107}, MRCLASS = {90C05}, MRNUMBER = {56 \#17791}, MRREVIEWER = {Jacques Dubois}, } @article{MR16:1054i, AUTHOR = {Dantzig, George B. and Orden, Alex and Wolfe, Philip}, TITLE = {The generalized simplex method for minimizing a linear form under linear inequality restraints}, JOURNAL = {Pacific J. Math.}, VOLUME = {5}, YEAR = {1955}, PAGES = {183--195}, MRCLASS = {65.0X}, MRNUMBER = {16,1054i}, MRREVIEWER = {A. J. Hoffman}, } @article{MR15:48d, AUTHOR = {Charnes, A.}, TITLE = {Optimality and degeneracy in linear programming}, JOURNAL = {Econometrica}, VOLUME = {20}, YEAR = {1952}, PAGES = {160--170}, MRCLASS = {90.0X}, MRNUMBER = {15,48d}, MRREVIEWER = {D. Gale}, } @inproceedings{MR15:354b, AUTHOR = {Charnes, A. and Lemke, C. E.}, TITLE = {Computational problems of linear programming}, BOOKTITLE = {Proceedings of the Association for Computing Machinery, Pittsburgh, 1952}, PAGES = {97--98}, PUBLISHER = {Richard Rimbach Associates, Pittsburgh, P. A.}, YEAR = {1952}, MRCLASS = {65.0X}, MRNUMBER = {15,354b}, } @article{MR18:514e, AUTHOR = {Beale, E. M. L.}, TITLE = {Cycling in the dual simplex algorithm}, JOURNAL = {Naval Res. Logist. Quart.}, VOLUME = {2}, YEAR = {1955}, PAGES = {269--275 (1956)}, MRCLASS = {65.3X}, MRNUMBER = {18,514e}, MRREVIEWER = {A. J. Hoffman}, } @article{interior, AUTHOR = {Forsgren, Anders and Gill, Philip E. and Wright, Margaret H.}, TITLE = {Interior Methods for Nonlinear Optimization}, JOURNAL = {{SIAM} Review}, VOLUME = {44}, YEAR = {2002}, NUMBER = {4}, PAGES = {525--598}, } @incollection{MR48:10492, AUTHOR = {Klee, Victor and Minty, George J.}, TITLE = {How good is the simplex algorithm?}, BOOKTITLE = {Inequalities, III (Proc. Third Sympos., Univ. California, Los Angeles, Calif., 1969; dedicated to the memory of Theodore S. Motzkin)}, PAGES = {159--175}, PUBLISHER = {Academic Press}, ADDRESS = {New York}, YEAR = {1972}, MRCLASS = {90C05}, MRNUMBER = {48 \#10492}, MRREVIEWER = {Robert G. Jeroslow}, } @article{khachian, AUTHOR = {Khachian, L. G.}, TITLE = {A Polynomial Algorithm for Linear Programming}, JOURNAL = {Dokl. Akad. Nauk SSSR}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {244}, YEAR = {1979}, NUMBER = {5}, PAGES = {1093--1096}, NOTE = {English translation in Soviet Math. Dokl. 20, 191-194, 1979}, } @article{MR86i:90072, AUTHOR = {Karmarkar, N.}, TITLE = {A new polynomial-time algorithm for linear programming}, JOURNAL = {Combinatorica}, FJOURNAL = {Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society}, VOLUME = {4}, YEAR = {1984}, NUMBER = {4}, PAGES = {373--395}, ISSN = {0209-9683}, CODEN = {COMBDI}, MRCLASS = {90C05}, MRNUMBER = {86i:90072}, MRREVIEWER = {K. G. Murty}, } @article{MR93b:90045, AUTHOR = {Ye, Y. Y.}, TITLE = {Extensions of the potential reduction algorithm for linear programming}, JOURNAL = {J. Optim. Theory Appl.}, FJOURNAL = {Journal of Optimization Theory and Applications}, VOLUME = {72}, YEAR = {1992}, NUMBER = {3}, PAGES = {487--498}, ISSN = {0022-3239}, CODEN = {JOTABN}, MRCLASS = {90C05 (90D05)}, MRNUMBER = {93b:90045}, MRREVIEWER = {Juan Garc{\'{\i}}a Laguna}, } @article{MR92h:90081, AUTHOR = {Ye, Yinyu}, TITLE = {An {$O(n\sp 3L)$} potential reduction algorithm for linear programming}, JOURNAL = {Math. Programming}, FJOURNAL = {Mathematical Programming}, VOLUME = {50}, YEAR = {1991}, NUMBER = {2, (Ser. A)}, PAGES = {239--258}, ISSN = {0025-5610}, CODEN = {MHPGA4}, MRCLASS = {90C05 (65K05)}, MRNUMBER = {92h:90081}, MRREVIEWER = {Adam Korytowski}, } @incollection{MR15:47k, AUTHOR = {Dantzig, George B.}, TITLE = {Maximization of a linear function of variables subject to linear inequalities}, BOOKTITLE = {Activity Analysis of Production and Allocation}, SERIES = {Cowles Commission Monograph No. 13}, PAGES = {339--347}, PUBLISHER = {John Wiley \& Sons Inc.}, ADDRESS = {New York, N. Y.}, YEAR = {1951}, MRCLASS = {90.0X}, MRNUMBER = {15,47k}, MRREVIEWER = {H. W. Kuhn}, } @article{MR2000f:68049, AUTHOR = {Feige, Uriel}, TITLE = {A threshold of {$\ln n$} for approximating set cover}, JOURNAL = {J. ACM}, FJOURNAL = {Journal of the ACM}, VOLUME = {45}, YEAR = {1998}, NUMBER = {4}, PAGES = {634--652}, ISSN = {0004-5411}, MRCLASS = {68Q17 (05C70)}, MRNUMBER = {2000f:68049}, MRREVIEWER = {Uwe Sch{\"o}ning}, } @incollection{MR1715654, AUTHOR = {Raz, Ran and Safra, Shmuel}, TITLE = {A sub-constant error-probability low-degree test, and a sub-constant error-probability {PCP} characterization of {NP}}, BOOKTITLE = {STOC '97 (El Paso, TX)}, PAGES = {475--484 (electronic)}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {1999}, MRCLASS = {68Q15}, MRNUMBER = {1 715 654}, } @inproceedings{MR1755538, AUTHOR = {Robins, Gabriel and Zelikovsky, Alexander}, TITLE = {Improved {S}teiner tree approximation in graphs}, BOOKTITLE = {Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 2000)}, PAGES = {770--779}, PUBLISHER = {ACM}, ADDRESS = {New York}, YEAR = {2000}, MRCLASS = {68R10 (68W25)}, MRNUMBER = {1 755 538}, } @incollection{MR98h:68105, AUTHOR = {Alimonti, Paola and Kann, Viggo}, TITLE = {Hardness of approximating problems on cubic graphs}, BOOKTITLE = {Algorithms and complexity (Rome, 1997)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1203}, PAGES = {288--298}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1997}, MRCLASS = {68Q25 (05C85 68R10)}, MRNUMBER = {98h:68105}, } @article{MR2000c:68107, AUTHOR = {Guha, Sudipto and Khuller, Samir}, TITLE = {Improved methods for approximating node weighted {S}teiner trees and connected dominating sets}, JOURNAL = {Inform. and Comput.}, FJOURNAL = {Information and Computation}, VOLUME = {150}, YEAR = {1999}, NUMBER = {1}, PAGES = {57--74}, ISSN = {0890-5401}, MRCLASS = {68R10 (68W25 68W40)}, MRNUMBER = {2000c:68107}, } @article{MR98m:68207, AUTHOR = {Guha, S. and Khuller, S.}, TITLE = {Approximation algorithms for connected dominating sets}, JOURNAL = {Algorithmica}, FJOURNAL = {Algorithmica. An International Journal in Computer Science}, VOLUME = {20}, YEAR = {1998}, NUMBER = {4}, PAGES = {374--387}, ISSN = {0178-4617}, CODEN = {ALGOEJ}, MRCLASS = {68R10 (68Q25)}, MRNUMBER = {98m:68207}, } @incollection{MR98g:68125, AUTHOR = {Guha, Sudipto and Khuller, Samir}, TITLE = {Approximation algorithms for connected dominating sets}, BOOKTITLE = {Algorithms---ESA '96 (Barcelona)}, SERIES = {Lecture Notes in Comput. Sci.}, VOLUME = {1136}, PAGES = {179--193}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1996}, MRCLASS = {68R10 (05C85 68Q25)}, MRNUMBER = {98g:68125}, } @article{MR80g:90082, AUTHOR = {Chv{\'a}tal, V.}, TITLE = {A greedy heuristic for the set-covering problem}, JOURNAL = {Math. Oper. Res.}, FJOURNAL = {Mathematics of Operations Research}, VOLUME = {4}, YEAR = {1979}, NUMBER = {3}, PAGES = {233--235}, ISSN = {0364-765X}, MRCLASS = {90C10}, MRNUMBER = {80g:90082}, MRREVIEWER = {Leon Cooper}, }