GRAPH PARTITION PROBLEMS WITH MINIMUM SIZE CONSTRAINTS

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[1]  Laurence A. Wolsey,et al.  Trees and Cuts , 1983 .

[2]  Francesco Maffioli,et al.  On the complexity of graph tree partition problems , 2004, Discret. Appl. Math..

[3]  Franz Rendl,et al.  Quadratic Knapsack Relaxations Using Cutting Planes , 1996, IPCO.

[4]  Alain Billionnet,et al.  Linear programming for the 0–1 quadratic knapsack problem , 1996 .

[5]  George L. Nemhauser,et al.  Min-cut clustering , 1993, Math. Program..

[6]  Martin W. P. Savelsbergh,et al.  A Branch-and-Price Algorithm for the Generalized Assignment Problem , 1997, Oper. Res..

[7]  Agha Iqbal Ali,et al.  Balanced spanning forests and trees , 1991, Networks.

[8]  Franz Rendl,et al.  Graph partitioning using linear and semidefinite programming , 2003, Math. Program..

[9]  S. Chopra.  On the spanning tree polyhedron , 1989 .

[10]  Jack Edmonds,et al.  Matching: A Well-Solved Class of Integer Linear Programs , 2001, Combinatorial Optimization.

[11]  Josep Domingo-Ferrer,et al.  Practical Data-Oriented Microaggregation for Statistical Disclosure Control , 2002, IEEE Trans. Knowl. Data Eng..

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

[13]  J. Mitchell.  Realignment in the National Football League: Did they do it right? , 2003 .

[14]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[15]  Manfred W. Padberg,et al.  The boolean quadric polytope: Some characteristics, facets and relatives , 1989, Math. Program..

[16]  Martin Grötschel,et al.  Facets of the Bipartite Subgraph Polytope , 1985, Math. Oper. Res..

[17]  D. Hochbaum,et al.  Forest Harvesting and Minimum Cuts: A New Approach to Handling Spatial Constraints , 1997 .

[18]  Michael A. Trick,et al.  Cliques and clustering: A combinatorial approach , 1998, Oper. Res. Lett..

[19]  Takeo Yamada,et al.  A branch-and-bound algorithm for the mini-max spanning forest problem , 1997 .

[20]  John E. Beasley,et al.  Heuristic algorithms for the unconstrained binary quadratic programming problem , 1998 .

[21]  John E. Mitchell,et al.  Computational Experience with an Interior Point Cutting Plane Algorithm , 1999, SIAM J. Optim..

[22]  Gordon Sande,et al.  Exact and Approximate Methods for Data Directed Microaggregation in One or More Dimensions , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[23]  Branch-and-cut Algorithms for Integer Programming, Branch-and-cut , 1998 .

[24]  C. Ribeiro,et al.  An optimal column-generation-with-ranking algorithm for very large scale set partitioning problems in traffic assignment , 1989 .

[25]  Refael Hassin,et al.  Approximation algorithms for maximum dispersion , 1997, Oper. Res. Lett..

[26]  Paolo Toth,et al.  Exact Solution of the Quadratic Knapsack Problem , 1999, INFORMS J. Comput..

[27]  Zsolt Tuza,et al.  Maximum cuts and largest bipartite subgraphs , 1993, Combinatorial Optimization.

[28]  W. Wilhelm.  A Technical Review of Column Generation in Integer Programming , 2001 .

[29]  M. R. Rao,et al.  The partition problem , 1993, Math. Program..

[30]  J. Mitchell,et al.  Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm , 2000 .

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

[32]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

[33]  Refael Hassin,et al.  Approximation Algorithms for Minimum Tree Partition , 1998, Discret. Appl. Math..

[34]  Michael A. Trick,et al.  A Column Generation Approach for Graph Coloring , 1996, INFORMS J. Comput..

[35]  Michael Jünger,et al.  Practical problem solving with cutting plane algorithms in combinatorialoptimization , 1993, Combinatorial Optimization.

[36]  Martin Grötschel,et al.  Facets of the clique partitioning polytope , 1990, Math. Program..

[37]  Sumitra Mukherjee,et al.  A Polynomial Algorithm for Optimal Microaggregation , 2001 .

[38]  Ulrich Faigle,et al.  A Lagrangian relaxation approach to the edge-weighted clique problem , 2001, Eur. J. Oper. Res..

[39]  Ali Ridha Mahjoub,et al.  On the cut polytope , 1986, Math. Program..

[40]  François Vanderbeck,et al.  Computational study of a column generation algorithm for bin packing and cutting stock problems , 1999, Math. Program..

[41]  Refael Hassin,et al.  Robust Matchings , 2002, SIAM J. Discret. Math..

[42]  Hanif D. Sherali,et al.  A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems , 1990, SIAM J. Discret. Math..

[43]  R. Gomory,et al.  Cutting Plane Algorithms for Integer Programming, Cutting Plane Algorithms , 1998 .

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

[45]  Martin W. P. Savelsbergh,et al.  MINTO, a mixed INTeger optimizer , 1994, Oper. Res. Lett..

[46]  George L. Nemhauser,et al.  Airline Crew Scheduling: A New Formulation and Decomposition Algorithm , 1997, Oper. Res..

[47]  Yoshiko Wakabayashi,et al.  A cutting plane algorithm for a clustering problem , 1989, Math. Program..

[48]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[49]  David P. Williamson,et al.  Approximating minimum-cost graph problems with spanning tree edges , 1994, Oper. Res. Lett..

[50]  Refael Hassin,et al.  Approximation algorithms for the metric maximum clustering problem with given cluster sizes , 2003, Oper. Res. Lett..

[51]  G. Nemhauser,et al.  An Optimization Based Heuristic for Political Districting , 1998 .

[52]  Ralph E. Gomory,et al.  A Linear Programming Approach to the Cutting Stock Problem---Part II , 1963 .

[53]  J. Mitchell.  Branch-and-Cut for the kway equipartition problem , 2000 .

[54]  Sungsoo Park,et al.  A polyhedral approach to edge coloring , 1991, Oper. Res. Lett..

[55]  Warren P. Adams,et al.  A hierarchy of relaxation between the continuous and convex hull representations , 1990 .

[56]  Michael Jünger,et al.  Experiments in quadratic 0–1 programming , 1989, Math. Program..

[57]  Leonid Khachiyan,et al.  A greedy heuristic for a minimum-weight forest problem , 1993, Oper. Res. Lett..

[58]  Ralph E. Gomory,et al.  An algorithm for integer solutions to linear programs , 1958 .

[59]  Antonio Sassano,et al.  The equipartition polytope. I: Formulations, dimension and basic facets , 1990, Math. Program..

[60]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[61]  P. Hammer,et al.  Quadratic knapsack problems , 1980 .