A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing

References

• Arenales M. N., Morábito R. An AND/OR graph approach to the solution of two-dimensional nonguillotine cutting problems. Eur. J. Oper. Res. (1995) 84:599–617Crossref, Google Scholar
• Beasley J. E. An exact two-dimensional nonguillotine cutting tree search procedure. Oper. Res. (1985) 33:49–64Link, Google Scholar
• Beasley J. E. OR-library: Distributing test problems by electronic mail. J. Oper. Res. Soc. (1990) 41:1069–1072Crossref, Google Scholar
• Biró M., Boros E. Network flows and nonguillotine cutting patterns. Eur. J. Oper. Res. (1984) 16:217–221Crossref, Google Scholar
• Christofides N., Whitlock C. An algorithm for two-dimensional cutting problems. Oper. Res. (1977) 25:31–44Link, Google Scholar
• Dowsland K. A. An exact algorithm for the pallet loading problem. Eur. J. Oper. Res. (1987) 31:78–84Crossref, Google Scholar
• Fekete S. P., Köhler E., Teich J. Higher-dimensional packing with order constraints. Algorithms and Data Structures (WADS 2001) (2001) 2125Providence, RI(Springer-Verlag, Heidelberg, Germany) 192–204Lecture Notes in Computer ScienceCrossref, Google Scholar
• Fekete S. P., Meijer H. Rectangle and box visibility graphs in 3D. Internat. J. Comput. Geometry Appl. (1999) 9:1–27Crossref, Google Scholar
• Fekete S. P., Schepers J. A new exact algorithm for general orthogonal d-dimensional knapsack problems. Algorithms—ESA '97 (1997a) 1284Graz, Austria(Springer-Verlag, Heidelberg, Germany) 144–156Lecture Notes in Computer ScienceCrossref, Google Scholar
• Fekete S. P., Schepers J. On higher-dimensional packing I: Modeling. (1997b) . Technical report, Center for Parallel Computing, University of Cologne. Available at the first author's web page.Google Scholar
• Fekete S. P., Schepers J. On higher-dimensional packing II: Bounds. (1997c) . Technical report, Center for Parallel Computing, University of Cologne. Available at the first author's web pageGoogle Scholar
• Fekete S. P., Schepers J. On higher-dimensional packing III: Exact algorithms. (1997d) . Technical report, Center for Parallel Computing, University of Cologne. Available at the first author's web page.Google Scholar
• Fekete S. P., Schepers J. An exact algorithm for higher-dimensional orthogonal packing. Oper. Res. (2004a) . ForthcomingGoogle Scholar
• Fekete S. P., Schepers J. A general framework for bounds for higher-dimensional packing probrems. Math. Methods Oper. Res. (2004b) Crossref, Google Scholar
• Garey M. R., Johnson D. S.Computers and Intractability: A Guide to the Theory of 𝒩𝒫-Completeness (1979) (Freeman, San Francisco, CA) Google Scholar
• Ghouilà-Houri A. Caractérization des graphes non orientés dont on peut orienter les arrêtes de manière à obtenir le graphe d'une relation d'ordre. C.R. Acad. Sci. Paris (1962) 254:1370–1371Google Scholar
• Gilmore P. C., Hoffmann A. J. A characterization of comparability graphs and of interval graphs. Canadian J. Math. (1964) 16:539–548Crossref, Google Scholar
• Golumbic M.Algorithmic Graph Theory and Perfect Graphs (1980) (Academic Press, New York) Crossref, Google Scholar
• Hadjiconstantinou E., Christofides N. An exact algorithm for general, orthogonal, two-dimensional knapsack problems. Eur. J. Oper. Res. (1995) 83:39–56Crossref, Google Scholar
• Jerrum M. R. A data structure for systems of orthogonal, non-overlapping rectangles. (1987) . Internal Report CSR-239-87, Department of Computer Science, University of Edinburgh, Edinburgh, U.K.Google Scholar
• Korte N., Möhring R. H. An incremental linear-time algorithm for recognizing interval graphs. SIAM J. Comput. (1989) 18:68–81Crossref, Google Scholar
• Lekkerkerker C. G., Boland J. C. Representation of a finite graph by a set of intervals on the real line. Fundamenta Math. (1962) 51:45–64Crossref, Google Scholar
• Martello S., Vigo D. Exact solution of the two-dimensional finite bin packing problem. Management Sci. (1998) 44:388–399Link, Google Scholar
• Martello S., Pisinger D., Vigo D. The three-dimensional bin packing problem. Oper. Res. (2000) 48:256–267Link, Google Scholar
• Nemhauser G., Wolsey L.Integer and Combinatorial Optimization (1988) (Wiley, Chichester, U.K.) Crossref, Google Scholar
• Padberg M. Packing small boxes into a big box. Math. Methods Oper. Res. (2000) 52:1–21Crossref, Google Scholar
• Schepers J.Exakte Algorithmen für orthogonale Packungsprobleme (1997) . Ph.D. thesis, Universität zu Köln, Cologne, GermanyGoogle Scholar
• Teich J., Fekete S. P., Schepers J. Optimal hardware reconfigurations techniques. J. Supercomputing (2001) 19:57–75Crossref, Google Scholar
• Wang P. Y. Two algorithms for constrained two-dimensional cutting stock problems. Oper. Res. (1983) 31:573–586Link, Google Scholar
• Wottawa M. Struktur und algorithmische Behandlung von praxisorientierten dreidimensionalen Packungs-problemen. (1996) . Ph.D. thesis, Universität zu Köln, Cologne, GermanyGoogle Scholar