The table placement problem: a research challenge at the EWI 2007

García, Sergio; Cacchiani, Valentina; Vanhaverbeke, Lieselot; Bischoff, Martin

doi:10.1007/s11750-012-0249-5

Cited by 2 publications

(4 citation statements)

References 14 publications

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“…Cycles with exactly 4 nodes -as of in lines (7)(8)(9), are labeled instantly. Lines (13)(14)(15)(16)(17)(18)(19) search for more complex patterns (e,g: F [3,5]). Lines (21)(22)(23) labels basic patterns in F .…”

Section: Appendixmentioning

confidence: 99%

“…Arranging seats around tables is not new for Operations Research as well. García et al [15], for instance, introduced a table placement problem aiming to maximize a measure of social benefit.…”

Section: Introductionmentioning

confidence: 99%

“…The corresponding CP model (11)(12)(13)(14)(15)(16)(17) describes (F * LP). We remark that alldifferent and card are typical CP operators on arrays of elements [4].…”

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confidence: 99%

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Merging Combinatorial Design and Optimization: the Oberwolfach Problem

Salassa¹,

Dragotto²,

Traetta³

et al. 2019

Preprint

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The Oberwolfach Problem OP (F ), posed by Gerhard Ringel in 1967, is a paradigmatic Combinatorial Design problem asking whether the complete graph K v decomposes into edge disjoint copies of a 2-regular graph F of order v. In Combinatorial Design Theory, so-called difference methods represent a well-known solution technique and construct solutions in infinitely many cases exploiting symmetric and balanced structures. This approach reduces the problem to finding a well-structured 2-factor which allows us to build solutions that we call 1-or 2-rotational according to their symmetries. We tackle OP by modeling difference methods with Optimization tools, specifically Constraint Programming (CP ) and Integer Programming (IP ), and correspondingly solve instances with up to v = 120 within 60s. In particular, we model the 2-rotational method by solving in cascade two subproblems, namely the binary and group labeling, respectively. A polynomial-time algorithm solves the binary labeling, while CP tackles the group labeling. Furthermore, we provide necessary conditions for the existence of some 1rotational solutions which stem from computational results. This paper shows thereby that both theoretical and empirical results may arise from the interaction between Combinatorial Design Theory and Operation Re- * Corresponding author.

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Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Merging Combinatorial Design and Optimization: the Oberwolfach Problem

Salassa¹,

Dragotto²,

Traetta³

et al. 2019

Preprint

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“…Although there exist papers in the literature that apply optimization methods to determine how many seats should be awarded to each party, such as Serafini (2012), to the best of our knowledge this paper is the first application of optimization methods to the allocation of physical seats within the congress. Several seat allocation problems have been studied previously, see for instance García et al (2014), but they are concerned with assigning individual people to seats, whereas in our problem the aim is to assign collections of seats to political parties. This fundamental difference means that, in practice, the problems have little in common.…”

Section: Literature Reviewmentioning

confidence: 99%

Congress seat allocation using mathematical optimization

Hales

García

2019

TOP

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After the 2015 Spanish general election a row erupted over the allocation of physical seats in the Congress of Deputies, with certain parties left feeling they possessed an inferior selection of seats compared to other parties. Using this as motivation, this paper considers how mathematical optimization can be used to generate seating plans for political chambers, an application that has not been considered before. As well as being in some way 'fair' to all parties, the seating plan should ensure that each block of seats is well-defined and compact. Two optimization models are formulated and, due to their complexity, heuristic methods are developed to find 'good' solutions. Analysis shows that the heuristics are able to produce visually appealing seating plans for basic cases, but problems can occur when there are additional requirements to be satisfied.

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The table placement problem: a research challenge at the EWI 2007

Cited by 2 publications

References 14 publications

Merging Combinatorial Design and Optimization: the Oberwolfach Problem

Merging Combinatorial Design and Optimization: the Oberwolfach Problem

Congress seat allocation using mathematical optimization

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