A Multistage Solution of the Template-Layout Problem

Haims, Murray J.; Freeman, Herbert

doi:10.1109/tssc.1970.300290

Cited by 62 publications

(6 citation statements)

References 5 publications

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“…The number of times an item of a particular type can be packed may be limited (bounded problem), or unlimited (unbounded problem). Haims and Freeman (1970) introduce a twodimensional problem of the SLOPP type which they name Template-Layout Problem. According to their general definition, a weakly heterogeneous set of regular or non-regular small items (''forms'') has to be cut from a single large rectangle such that the value of the cut items is maximised.…”

Section: Single Large Object Placement Problemmentioning

confidence: 99%

An improved typology of cutting and packing problems

Wäscher

Haußner

Schumann

2007

European Journal of Operational Research

1,227

602

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Section: Single Large Object Placement Problemmentioning

confidence: 99%

An improved typology of cutting and packing problems

Wäscher

Haußner

Schumann

2007

European Journal of Operational Research

1,227

602

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“…However, even in those cases in which the total address space must be large because of the problem size, it is often possible to subdivide the space into chunks such that the number of pointer references within the chunk greatly exceed those that go out of the chunk. For example this has been shown to be the case in a paged LISP (Bobrow and Murphy [1]) for a number of different problems, as long as care is taken to construct pointer pairs ("cons cells") on the same page as their contents. In this LISP, interpage pointers were avoided when possible to minimize the working set size of the paged system.…”

Section: Data Compressionmentioning

confidence: 99%

“…The obvious extension of this principle is to allow association with any structure (as specified by its machine address) a full pointer to another structure. This feature has been implemented by the author in Interlisp (Bobrow and Murphy [1], Teitelman [3]) thus allowing arbitrary structures in LISP to have a 415 property list without having to allocate a cell in each potential structure for such a property list. It also allows several different types of property list without interference and without confusion for programs which wish to ignore the presence of this information.…”

Section: Marking Reentrant Structures Suppose a Linkedmentioning

confidence: 99%

A note on hash linking

Bobrow

1975

Commun. ACM

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In current machine designs, a machine address gives the user direct access to a single piece of information, namely the contents of that machine word. This note is based on the observation that it is often useful to associate additional information, with some (relatively few) address locations determined at run time, without the necessity of preallocating the storage at all possible such addresses. That is, it can be useful to have an effective extra bit, field, or address in some words without every word having to contain a bit (or bits) to mark this as a special case. The key idea is that this extra associated information can be found by a table search. Although it could be found by any search technique (e.g. linear, binary sorted, etc.), we suggest that an appropriate low overhead mechanism is to use hash search on a table in which the key is the address of the cell to be augmented.

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“…2 Containment is the`feasibility question' for minimal enclosure, and thus the appropriate complexity question is the hardness of containment. Techniques of combinatorial optimization such as integer or dynamic programming have been successfully applied to NP-complete packing problems such as layout of rectangles (Gilmore and Gomory, 1965;Adamowicz and Albano, 1976;Haims and Freeman, 1970). However, non-convex shapes appear to be too irregular to permit direct application of these techniques.…”

Section: Introductionmentioning

confidence: 99%

Translational polygon containment and minimal enclosure using mathematical programming

Milenkovic

1999

International Transactions in Operational Research

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A new algorithm is given for the two-dimensional translational containment problem: ®nd translations for k polygons which place them inside a polygonal container without overlapping. Both the polygons and the container can be non-convex. The algorithm is based on mathematical programming principles. The containment algorithm is generalized to solve minimal enclosure problems: ®nd the minimal area enclosing square or minimal area enclosing rectangle for k translating polygons. The containment algorithm consists of new algorithms for restriction, evaluation, and subdivision of two-dimensional con®guration spaces. Restriction establishes lower bounds through relaxation and the solution of linear programs. Evaluation establishes upper bounds by ®nding potential solutions. Subdivision branches, when necessary, by introducing a cutting plane. The algorithm shows that either the upper bound of the objective (overlap) is exactly zero or the lower bound is greater than zero. Hence, it gives an exact solution to the containment problem. Experiments show that new containment algorithm clearly outperforms purely geometric containment algorithms. For data sets from the apparel industry, it can solve containment for up to ten nonconvex polygons in practice. An implementation of the algorithm given in this paper has been licensed by Gerber Garment Technologies, the largest provider of textile CAD/CAM software in the Intl.

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A Multistage Solution of the Template-Layout Problem

Cited by 62 publications

References 5 publications

An improved typology of cutting and packing problems

An improved typology of cutting and packing problems

A note on hash linking

Translational polygon containment and minimal enclosure using mathematical programming

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