Exact Algorithms for a Loading Problem with Bounded Clique Width

Moonen, Linda; Spieksma, Frits

doi:10.1287/ijoc.1040.0124

Cited by 10 publications

(7 citation statements)

References 26 publications

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“…We use 3 different data sets for the experiments. The first data set contains 50 real-world instances provided to us by Bruynzeel Storage Systems, the second data set contains 50 randomly generated instances, and the third data set contains 50 randomly generated instances that have small clique-width (see Moonen and Spieksma (2005)). The problem instances for all three data sets contain between 20 and 200 elements.…”

Section: Computational Resultsmentioning

confidence: 99%

“…Another application of MWPB is described in Moonen and Spieksma (2005). Given are a number of rectangular shaped boxes, each with a given length i and width w i .…”

Section: Applicationsmentioning

confidence: 99%

“…In some applications, for example in the field of pallet loading problems as discussed in Moonen and Spieksma (2005), the items are allowed to be rotated (i.e., the length and the width of an item are swapped) if that allows us to find a better solution. It is not difficult to exhibit instances where allowing rotation improves the solution value.…”

Section: Rotation Problemmentioning

confidence: 99%

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Partitioning a weighted partial order

Moonen

Spieksma

2007

J Comb Optim

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The problem of partitioning a partially ordered set into a minimum number of chains is a well-known problem. In this paper we study a generalization of this problem, where we not only assume that the chains have bounded size, but also that a weight w i is given for each element i in the partial order such that w i ≤ w j if i ≺ j. The problem is then to partition the partial order into a minimum-weight set of chains of bounded size, where the weight of a chain equals the weight of the heaviest element in the chain. We prove that this problem is APX-hard, and we propose and analyze lower bounds for this problem. Based on these lower bounds, we exhibit a 2-approximation algorithm, and show that it is tight. We report computational results for a number of real-world and randomly generated problem instances.

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Section: Computational Resultsmentioning

confidence: 99%

“…Another application of MWPB is described in Moonen and Spieksma (2005). Given are a number of rectangular shaped boxes, each with a given length i and width w i .…”

Section: Applicationsmentioning

confidence: 99%

Section: Rotation Problemmentioning

confidence: 99%

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Partitioning a weighted partial order

Moonen

Spieksma

2007

J Comb Optim

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“…Courcelle and Engelfriet mention in [45, p. 504] that MSO model-checking for decomposable graphs (e.g., [36,48]) has been cited in different fields of applied computer science, such as, e.g., computational biology [130], computational linguistics [111], database querying [9], logistics [139], telecommunications [136], quantum computing [178], or the aforementioned [174] on register allocation for compilers, to name a few. It is therefore of great interested to make Courcelle's Theorem useful in practice.…”

Section: Courcelle's Theorem In Practicementioning

confidence: 99%

Practical algorithms for MSO model-checking on tree-decomposable graphs

Langer

Reidl

Rossmanith

et al. 2014

Computer Science Review

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In this survey, we review practical algorithms for graph-theoretic problems that are expressible in monadic second-order logic. Monadic second-order (MSO) logic allows quantifications over unary relations (sets) and can be used to express a host of useful graph properties such as connectivity, c-colorability (for a fixed c), Hamiltonicity and minor inclusion. A celebrated theorem in this area by Courcelle states that any graph problem expressible in MSO can be solved in linear time on graphs that admit a tree-decomposition of constant width. Courcelle's Theorem has been used thus far as a theoretic tool to establish that linear-time algorithms exist for graph problems by demonstrating that the problem in question is expressible by an MSO formula. A straightforward implementation of the algorithm in the proof of Courcelle's Theorem is useless as it runs into space-explosion problems even for small values of treewidth. Of late, there have been several attempts to circumvent these problems and we review some of these in this survey. This survey also introduces the reader to the notions of tree-decompositions and the basics of monadic second order logic.

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“…Also, the randomly generated instances with small clique-width can be solved efficiently by the enumeration algorithm (95% of these instances are solved in less than 1 s), but the random instances cannot be solved efficiently, due to the large number of different lengths in the input. For more details we refer to Moonen and Spieksma (2006).…”

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confidence: 99%

Algorithms for some graph theoretical optimization problems

Moonen

2006

4OR

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This is a summary of the main results presented in the author's PhD thesis. This thesis, written in English, was supervised by Frits Spieksma and defended on September 23, 2005 at the Katholieke Universiteit Leuven. A copy of the thesis is available from the authors website (http://www.econ. kuleuven.be/linda.moonen/public/). The thesis can be roughly split into two parts. The first part is dedicated to the problem of partitioning partially ordered sets into chains of limited size. The second part deals with the structure and the connectivity of the Internet.Keywords Integer programming · Branch-and-price algorithms · Partially ordered sets MSC classification 05C85 Partitioning a partially ordered setThe problem of partitioning a partially ordered set X into a minimal number of chains, such that each element belongs to at least one chain, is a basic and fundamental problem in combinatorial optimization and discrete mathematics. Dilworth (1950) showed that it is solvable in polynomial time, and that the minimum number of chains needed to cover all elements of X is equal to the value of a maximum antichain. We generalize this problem by assuming that the chains must have bounded size; the resulting problem is shown to be

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Exact Algorithms for a Loading Problem with Bounded Clique Width

Cited by 10 publications

References 26 publications

Partitioning a weighted partial order

Partitioning a weighted partial order

Practical algorithms for MSO model-checking on tree-decomposable graphs

Algorithms for some graph theoretical optimization problems

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