Creating seating plans: a practical application

Lewis, Rhyd; Carroll, Fiona

doi:10.1057/jors.2016.34

Cited by 17 publications

(15 citation statements)

References 8 publications

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“…If a move at iteration l of the algorithm is performed that transfers vertex v from S i to S j , then element T vi is set to l + t. This is interpreted to mean that, for the next t iterations, all solutions involving the assignment of v to colour i are considered tabu and are not permitted unless the above aspiration criterion is met. To determine the value of t, we use previous studies on graph partitioning problems as a guide (Blöchliger and Zufferey, 2008;Lewis and Carroll, 2016). These suggest that t should be a random variable whose value is determined based on the current solution's quality.…”

Section: Tabu Searchmentioning

confidence: 99%

“…Solving the MHV problem leads to a solution in which the number of people in teams containing all of their friends is maximised. Similar tasks might also arise in the design of seating plans for large social events such as a wedding or gala dinner (Lewis and Carroll, 2016). More generally, the MHV problem has applications in clustering based problems; specifically, where some objects have been assigned to clusters, and the aim is to assign the remaining objects to these clusters such that related objects occur in the same cluster (Everitt et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

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Tackling the maximum happy vertices problem in large networks

2020

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In this paper we consider a variant of graph colouring known as the Maximum Happy Vertices (MHV) problem. This problem involves taking a graph in which a subset of the vertices have been preassigned to colours. The objective is to then colour the remaining vertices such that the number of happy vertices is maximised, where a vertex is considered happy only when it is assigned to the same colour as all of its neighbours. We design and test a tabu search approach, which is compared to two existing state of the art methods. We see that this new approach is particularly suited to larger problem instances and finds very good solutions in very short time frames. We also propose a algorithm to find upper bounds for the problem efficiently. Moreover, we propose an algorithm for imposing additional precoloured vertices and are hence able to significantly reduce the solution space. Finally, we present an analysis of this problem and use probabilistic arguments to characterise problem hardness.

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Section: Tabu Searchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tackling the maximum happy vertices problem in large networks

2020

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“…In our case S bsf is found by executing both the GREEDY-MHV and GROWTH-MHV algorithms and taking the best of the returned solutions. Steps (4) to (13) then contain the main body of the algorithm. In each iteration n a solutions are generated probabilistically using the GENERATE-SOLUTION procedure and, if not already present, the components of these solutions are added to the set C ′ .…”

Section: Scaling-up Issues and A Metaheuristic Approachmentioning

confidence: 99%

“…In the case of vertex colouring, this can be useful in areas such as social networking, where we might be interested in assigning groups of related people (vertices) to the same resource, such as a team or a task. Recent studies have also looked at how we might design seating plans for large social gatherings such as weddings, where the aim is simultaneously place people with their friends, but apart from their adversaries [7,13].…”

Section: Introductionmentioning

confidence: 99%

Finding happiness: An analysis of the maximum happy vertices problem

Lewis¹,

Thiruvady

Morgan

2019

Computers & Operations Research

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The maximum happy vertices problem involves determining a vertex colouring of a graph such that the number of vertices assigned to the same colour as all of their neighbours is maximised. This problem is trivial if no vertices are precoloured, though in general it is NP-hard. In this paper we derive a number of upper and lower bounds on the number of happy vertices that are achievable in a graph and then demonstrate how certain problem instances can be broken up into smaller subproblems. Four different algorithms are also used to investigate the factors that make some problem instances more difficult to solve than others. In general, we find that the most difficult problems are those with relatively few edges and/or a small number of precoloured vertices. Ideas for future research are also discussed.

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“…Here, each location is represented by a vertex, an edge exists between two vertices if their respective locations are within a certain proximity of one another (which could lead to interference) and colours represent the communication frequencies. Other examples include register allocation (Chaitin 1982), tournament scheduling (Costa 1995), exam timetabling (Erben 2001;Qu et al 2009), designing seating plans (Lewis and Carroll 2016) and grouping people in social networks (Tantipathananandh et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Tackling the edge dynamic graph colouring problem with and without future adjacency information

2017

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Many real world operational research problems, such as frequency assignment and exam timetabling, can be reformulated as graph colouring problems (GCPs). Most algorithms for the GCP operate under the assumption that its constraints are fixed, allowing us to model the problem using a static graph. However, in many real-world cases this does not hold and it is more appropriate to model problems with constraints that change over time using an edge dynamic graph. Although exploring methods for colouring dynamic graphs has been identified as an area of interest with many real-world applications, to date, very little literature exists regarding such methods. In this paper we present several heuristic methods for modifying a feasible colouring at time-step t into an initial, but not necessarily feasible, colouring for a "similar" graph at time-step t + 1. We will discuss two cases; (1) where changes occur at random, and (2) where probabilistic information about future changes is provided. Experimental results are also presented and the benefits of applying these particular modification methods are investigated.

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Creating seating plans: a practical application

Cited by 17 publications

References 8 publications

Tackling the maximum happy vertices problem in large networks

Tackling the maximum happy vertices problem in large networks

Finding happiness: An analysis of the maximum happy vertices problem

Tackling the edge dynamic graph colouring problem with and without future adjacency information

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