Counting Hexagonal Patches and Independent Sets in Circle Graphs

Bonsma, Paul; Breuer, Felix

doi:10.1007/978-3-642-12200-2_52

Cited by 3 publications

(4 citation statements)

References 26 publications

(48 reference statements)

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“…Solving the subproblem The problem of finding variables with negative reduced costs is almost equivalent to finding a maximum weight independent set in a circle graph, which can be solved in polynomial time by dynamic programming [1,12]. A circle graph is an intersection graph of chords of a a circle, two vertices/chords are adjacent if and only if they intersect.…”

Section: Formulation As An Ilpmentioning

confidence: 99%

A Branch and Price Procedure for the Container Premarshalling Problem

Brink

Zwaan

2014

Algorithms - ESA 2014

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During the loading phase of a vessel, only the containers that are on top of their stack are directly accessible. If the container that needs to be loaded next is not the top container, extra moves have to be performed, resulting in an increased loading time. One way to resolve this issue is via a procedure called premarshalling. The goal of premarshalling is to reshuffle the containers into a desired lay-out prior to the arrival of the vessel, in the minimum number of moves possible. This paper presents an exact algorithm based on branch and bound, that is evaluated on a large set of instances. The complexity of the premarshalling problem is also considered, and this paper shows that the problem at hand is NPhard, even in the natural case of stacks with fixed height.

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Section: Formulation As An Ilpmentioning

confidence: 99%

A Branch and Price Procedure for the Container Premarshalling Problem

Brink

Zwaan

2014

Algorithms - ESA 2014

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“…Our algorithm has complexity n O( f 5 ) . An algorithm with complexity f ( f 5 )n O (1) for some computable function f (a fixed parameter tractable (FPT) algorithm) would be preferable, but we do not know whether such an algorithm is possible.…”

Section: Question 4 Is Fullerene Patch -Boundary Code Np-hard?mentioning

confidence: 99%

“…Their construction can be extended to show that exponentially many solutions are possible. Nevertheless, we have shown in [1] that in this case counting can be done in polynomial time:…”

Section: Introductionmentioning

confidence: 99%

Finding Fullerene Patches in Polynomial Time

Bonsma

Breuer

2009

Algorithms and Computation

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Abstract. We consider the following question, motivated by the enumeration of fullerenes. A fullerene patch is a 2-connected plane graph G in which inner faces have length 5 or 6, non-boundary vertices have degree 3, and boundary vertices have degree 2 or 3. The degree sequence along the boundary is called the boundary code of G. We show that the question whether a given sequence S is a boundary code of some fullerene patch can be answered in polynomial time when such patches have at most five 5-faces. We conjecture that our algorithm gives the correct answer for any number of 5-faces, and sketch how to extend the algorithm to the problem of counting the number of different patches with a given boundary code.

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“…Without condition (b) this problem would be equivalent to finding a maximum weight independent set in a circle graph, which can be solved in polynomial time by dynamic programming[10,75].A circle graph is an intersection graph of chords of a circle, and two vertices/chords are adjacent if and only if they intersect. Circle graphs can equivalently be defined as the overlap graph of a set of intervals.…”

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confidence: 99%

Essays on practical computational methods for operational planning

Brink

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Counting Hexagonal Patches and Independent Sets in Circle Graphs

Cited by 3 publications

References 26 publications

A Branch and Price Procedure for the Container Premarshalling Problem

A Branch and Price Procedure for the Container Premarshalling Problem

Finding Fullerene Patches in Polynomial Time

Essays on practical computational methods for operational planning

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