Discrete extremal problems

Precise and heuristic algorithms for solving various classes of discrete extremal problems are considered as are the relations between the class of discrete extremal problems and linear programming and are extremal problems from the point of view of the theory of polynomial completeness. A class of bottleneck optimization problems and stability in discrete extremal problems with a linear object function are also considered.

[1]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[2]  W. T. Tutte A Class Of Abelian Groups , 1956, Canadian Journal of Mathematics.

[3]  J. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[4]  I. Heller Neighbor relations on the convex of cyclic permutations. , 1956 .

[5]  I. Heller On linear systems with integral valued solutions. , 1957 .

[6]  R. Rado Note on Independence Functions , 1957 .

[7]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[9]  Y. I. Zhuravlev Local algorithms for the calculation of information. Part I , 1965 .

[10]  P. Camion Characterization of totally unimodular matrices , 1965 .

[11]  Jack Edmonds,et al.  Maximum matching and a polyhedron with 0,1-vertices , 1965 .

[12]  V. S. Mikhalevich Sequential optimization algorithms and their application. Part I , 1965 .

[13]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[14]  Egon Balas,et al.  Discrete Programming by the Filter Method , 1967, Oper. Res..

[15]  G. Dantzig,et al.  Integral Extreme Points , 1968 .

[16]  D. Suprunenko The values of a linear form on a set of permutations , 1968 .

[17]  R. Chandrasekaran Total Unimodularity of Matrices , 1969 .

[18]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[19]  Jack Edmonds,et al.  Matroids and the greedy algorithm , 1971, Math. Program..

[20]  D. R. Fulkerson,et al.  Blocking and anti-blocking pairs of polyhedra , 1971, Math. Program..

[21]  W. T. Tutte Introduction to the theory of matroids , 1971 .

[22]  Patrick D. Krolak,et al.  A man-machine approach toward solving the traveling salesman problem , 1970, DAC '70.

[23]  V. A. Emelichev,et al.  Discrete optimization. Sequential decision schemes. I , 1971, Cybernetics.

[24]  Jaroslav Morávek A localization problem in geometry and complexity of discrete programming , 1972, Kybernetika.

[25]  D. R. Fulkerson,et al.  Anti-blocking polyhedra , 1972 .

[26]  V. Emelichev Discrete optimization. Sequential schemes of solution. II , 1972 .

[27]  László Lovász,et al.  Normal hypergraphs and the perfect graph conjecture , 1972, Discret. Math..

[28]  Michael O. Rabin,et al.  Proving Simultaneous Positivity of Linear Forms , 1972, J. Comput. Syst. Sci..

[29]  D. J. A. Welsh,et al.  A greedy algorithm for solving a certain class of linear programmes , 1973, Math. Program..

[30]  Vasek Chvátal,et al.  Edmonds polytopes and a hierarchy of combinatorial problems , 1973, Discret. Math..

[31]  G. Nemhauser,et al.  A Survey of Integer Programming Emphasizing Computation and Relations among Models , 1973 .

[32]  Philip M. Spira,et al.  A New Algorithm for Finding all Shortest Paths in a Graph of Positive Arcs in Average Time 0(n2 log2n) , 1973, SIAM J. Comput..

[33]  Vasek Chvátal,et al.  Edmonds polytopes and weakly hamiltonian graphs , 1973, Math. Program..

[34]  D. Suprunenko,et al.  Problem of appointments and minimization of the sums of linear forms on a symmetric group , 1973 .

[35]  Manfred W. Padberg,et al.  On the facial structure of set packing polyhedra , 1973, Math. Program..

[36]  A. Tucker,et al.  The Strong Perfect Graph Conjecture for Planar Graphs , 1973, Canadian Journal of Mathematics.

[37]  J. Anthonisse,et al.  Are polynomial algorithms really good , 1974 .

[38]  J. Edmonds,et al.  Facets of I-matching polyhedra , 1974 .

[39]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.

[40]  Leslie E. Trotter,et al.  Properties of vertex packing and independence system polyhedra , 1974, Math. Program..

[41]  M. R. Rao,et al.  The travelling salesman problem and a class of polyhedra of diameter two , 1974, Math. Program..

[42]  M. Balinski,et al.  On the Assignment Polytope , 1974 .

[43]  D. R. Fulkerson,et al.  On balanced matrices , 1974 .

[44]  M. Padberg Perfect Zero-One Matrices — II , 1974 .

[45]  Manfred W. Padberg,et al.  Perfect zero–one matrices , 1974, Math. Program..

[46]  Rainer E. Burkard,et al.  Kombinatorische optimierung in halbgruppen , 1975 .

[47]  R.E. Ladner,et al.  A Comparison of Polynomial Time Reducibilities , 1975, Theor. Comput. Sci..

[48]  A. Pan,et al.  On Finding and Updating Spanning Trees and Shortest Paths , 1975, SIAM J. Comput..

[49]  J. Maurras Some Results on the Convex Hull of the Hamiltonian Cycles of Symetric Complete Graphs , 1975 .

[50]  Martin Grötschel,et al.  Partial linear characterizations of the asymmetric travelling salesman polytope , 1975, Math. Program..

[51]  Oscar H. Ibarra,et al.  Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems , 1975, JACM.

[52]  Vaughan R. Pratt,et al.  Every Prime has a Succinct Certificate , 1975, SIAM J. Comput..

[53]  Richard M. Karp,et al.  On the Computational Complexity of Combinatorial Problems , 1975, Networks.

[54]  R. Solovay,et al.  Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question , 1975 .

[55]  Certain class of problems in integral linear programming , 1975 .

[56]  Leslie E. Trotter,et al.  Vertex packings: Structural properties and algorithms , 1975, Math. Program..

[57]  Eugene L. Lawler,et al.  Matroid intersection algorithms , 1975, Math. Program..

[58]  J. Edmonds Some Well-Solved Problems in Combinatorial Optimization , 1975 .

[59]  Sartaj Sahni,et al.  Approximate Algorithms for the 0/1 Knapsack Problem , 1975, JACM.

[60]  Richard E. Ladner,et al.  On the Structure of Polynomial Time Reducibility , 1975, JACM.

[61]  M. Padberg Characterisations of Totally Unimodular, Balanced and Perfect Matrices , 1975 .

[62]  V. Chvátal On certain polytopes associated with graphs , 1975 .

[63]  R. Brualdi,et al.  Convex polyhedra of doubly stochastic matrices—IV , 1976 .

[64]  David S. Johnson,et al.  Stockmeyer: some simplified np-complete graph problems , 1976 .

[65]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[66]  Gary L. Miller Riemann's Hypothesis and Tests for Primality , 1976, J. Comput. Syst. Sci..

[67]  Claus Kastning,et al.  Integer programming and related areas : a classified bibliography , 1976 .

[68]  M. Padberg Almost integral polyhedra related to certain combinatorial optimization problems , 1976 .

[69]  David S. Johnson,et al.  The Complexity of Near-Optimal Graph Coloring , 1976, J. ACM.

[70]  J. Hopcroft,et al.  Independence results in computer science , 1976, SIGA.

[71]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[72]  David P. Dobkin A Nonlinear Lower Bound on Linear Search Tree Programs for Solving Knapsack Problems , 1976, J. Comput. Syst. Sci..

[73]  Richard J. Lipton,et al.  A Lower Bound of ½n² on Linear Search Programs for the Knapsack Problem , 1976, MFCS.

[74]  Manfred W. Padberg,et al.  A note on the total unimodularity of matrices , 1976, Discret. Math..

[75]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems: an annotated bibliography , 1976 .

[76]  A. Bagchi,et al.  Neighborhood Search Algorithms for Guaranteeing Optimal Traveling Salesman Tours Must Be Inefficient , 1976, J. Comput. Syst. Sci..

[77]  E. Balas,et al.  Set Partitioning: A survey , 1976 .

[78]  Robert S. Garfinkel,et al.  Bottleneck linear programming , 1976, Math. Program..

[79]  Ronald L. Rivest,et al.  On Recognizing Graph Properties from Adjacency Matrices , 1976, Theor. Comput. Sci..

[80]  Giorgio Ausiello,et al.  Classes of Structurally Isomorphic {NP}-Optimization Problems , 1977, MFCS.

[81]  Giorgio Ausiello On the Structure and Properties of NP-Complete Problems and Their Associated Optimization Problems , 1977, MFCS.

[82]  Volker Strassen,et al.  A Fast Monte-Carlo Test for Primality , 1977, SIAM J. Comput..

[83]  J. Edmonds,et al.  A Min-Max Relation for Submodular Functions on Graphs , 1977 .

[84]  Richard A. Brualdi,et al.  Convex polyhedra of doubly stochastic matrices: II. Graph of Omegan , 1977, J. Comb. Theory, Ser. B.

[85]  M. Padberg On the Complexity of Set Packing Polyhedra , 1977 .

[86]  Martin Grötschel,et al.  Lineare Charakterisierungen von Travelling Salesman Problemen , 1977, Math. Methods Oper. Res..

[87]  Zun problem der optimalen standardisierung , 1977 .

[88]  John S. Carson,et al.  A Note on Spira's Algorithm for the All-Pairs Shortest-Path Problem , 1977, SIAM J. Comput..

[89]  Juris Hartmanis,et al.  On Isomorphisms and Density of NP and Other Complete Sets , 1977, SIAM J. Comput..

[90]  Janos Simon,et al.  On the Difference Between One and Many (Preliminary Version) , 1977, ICALP.

[91]  Y. I. Zhuravlev Correct algebras over sets of incorrect (Heuristic) algorithms. II , 1978 .

[92]  Richard A. Brualdi,et al.  Convex Polyhedra of Doubly Stochastic Matrices. I. Applications of the Permanent Function , 1977, J. Comb. Theory A.

[93]  Frank David John Dunstan An Algorithm for Solving a Resource Allocation Problem , 1977 .

[94]  Richard M. Karp,et al.  Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane , 1977, Math. Oper. Res..

[95]  Shlomo Moran,et al.  Non Deterministic Polynomial Optimization Problems and their Approximations , 1977, Theoretical Computer Science.

[96]  Vasek Chvátal,et al.  Determining the Stability Number of a Graph , 1976, SIAM J. Comput..

[97]  Richard A. Brualdi,et al.  Convex Polyhedra of Doubly Stochastic Matrices III. Affine and Combinatorial Properties of Omegan , 1977, J. Comb. Theory, Ser. A.

[98]  Sartaj Sahni,et al.  General Techniques for Combinatorial Approximation , 1977, Oper. Res..

[99]  DAVID DOBKIN,et al.  A Lower Bound of the ½n² on Linear Search Programs for the Knapsack Problem , 1978, J. Comput. Syst. Sci..

[100]  R. Brualdi,et al.  On the truncated assignment polytope , 1978 .

[101]  G. L. Nemhauser,et al.  Tight bounds for christofides' traveling salesman heuristic , 1978, Math. Program..

[102]  Volker Strassen,et al.  Erratum: A Fast Monte-Carlo Test for Primality , 1978, SIAM J. Comput..

[103]  R. Nigmatullin Approximate algorithms with bounded absolute error for discrete extremal problems , 1978 .

[104]  Shlomo Moran,et al.  Non Deterministic Polynomial Optimization Problems and their Approximations , 1977, Theor. Comput. Sci..

[105]  R. Cole Two Problems in Graph Theory , 1982 .

[106]  Daniel J. Rosenkrantz,et al.  An analysis of several heuristics for the traveling salesman problem , 2013, Fundamental Problems in Computing.