Some Applications of Graph Theory

Roberts, Fred S.

doi:10.1142/9789812799890_0008

Cited by 4 publications

(5 citation statements)

References 124 publications

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“…The seven specialists described in Section 3.2 were again consulted to define the criteria's weights at this stage. The Roberts matrix [42] was first used to determine the order of relevance of the criteria and sub-criteria. Then, the swing weights methodology was applied, which seeks to capture the specialists' preferences by balancing the weights of the criteria.…”

Section: Definition Of Weights To Defined Criteriamentioning

confidence: 99%

“…After using the Roberts matrix [42], the swing weights system was applied to determine the weights the criteria and sub-criteria. Each specialist awarded a score of 100 to the most relevant criterion or sub-criterion (an item that received a higher score during application of the Roberts matrix) and awarded a proportional score to the remainder compared to the most relevant criterion or sub-criterion.…”

Section: Replacement Ratesmentioning

confidence: 99%

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Measuring the Attractiveness of Cities to Receive Investments in Regional Airport Infrastructure

et al. 2022

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The vast Brazilian territory and the accelerated economic growth of the cities of the country’s interior in recent years have created a favourable environment for the expansion of regional aviation. In 2015, the Brazilian Government launched a program of investments in regional airports equipping them to receive commercial flights. However, the economic crisis and the scarcity of resources drive the prioritisation of projects with a greater economic and social return. This article aims to present a multicriteria decision aid (MCDA) model to measure cities’ attractiveness to receive investments in regional airports. The MCDA approach can deal with multiple indicators and different points of view and provide systematised steps for supporting decision-makers. For this purpose, we selected 12 criteria among the evaluation parameters identified in the literature, which led to the construction of the evaluation model and elaborating the ranking of the localities participating in the investment program. This study can contribute scientifically by proposing the use of an MCDA approach to support decisions related to logistics and infrastructure. It can help managers and practitioners provide a structured and systematised model to address decisions related to airport investments.

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Section: Definition Of Weights To Defined Criteriamentioning

confidence: 99%

Section: Replacement Ratesmentioning

confidence: 99%

Measuring the Attractiveness of Cities to Receive Investments in Regional Airport Infrastructure

et al. 2022

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“…References G is a Proper Interval Graph. [14,29,30,31,32] G is a Unit Interval Graph G is claw-free, i.e., G does not contain K 1,3 as an induced subgraph. For all v ∈ V , elements of [7,8,9,14] consecutive for some ordering of V (closed neighborhood condition).…”

Section: Index Propertiesmentioning

confidence: 99%

Characterization and Recognition of Proper Tagged Probe Interval Graphs

Paul

Ghosh

Chakraborty

et al. 2019

Advances in Intelligent Systems and Computing

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Interval graphs were used in the study of the human genome project by the famous molecular biologist Benzer. Later on probe interval graphs were introduced by Zhang as a generalization of interval graphs for the study of cosmid contig mapping of DNA. Further research in this area required more useful and cost effective tools. The concept of tagged probe interval graphs (briefly, TPIG) is motivated from this point of view, where the set of vertices is partitioned into two sets, namely, probes and nonprobes and there is an interval on the real line corresponding to each vertex. The graph has an edge between two probe vertices if their corresponding intervals intersect, has an edge between a probe vertex and a nonprobe vertex if the interval corresponding to a nonprobe vertex contains at least one endpoint of the interval corresponding to a probe vertex and the set of nonprobe vertices is an independent set.In this paper, we consider a natural subclass of TPIG, namely, the class of proper tagged probe interval graphs (in short PTPIG). We present characterization theorem and a linear time recognition algorithm for PTPIG. To obtain this characterization theorem we introduce canonical sequences for proper interval graphs. In the recognition algorithm for PTPIG, we introduce and solve a variation of consecutive 1's problem, namely, oriented consecutive 1's problem and some variations of PQ-tree algorithm. We also discuss the interrelations between the classes of PTPIG and TPIG with probe interval graphs and probe proper interval graphs.

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“…Interval graphs have many real applications in diverse areas including genetics [3], economics, and archaeology [37,38]. According to Golumbic [19], many real-world applications involve solving problems on graphs which are either interval graphs themselves or are related to interval graphs in a natural way.…”

Section: Introductionmentioning

confidence: 99%

$${\mathcal {U}}$$-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

2021

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Interval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs—a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a richer class of graphs. In particular, mixed unit interval graphs may contain a claw as an induced subgraph, as opposed to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs and demonstrate the advantages of this generalized model by providing a subexponential-time algorithm for solving the MaxCut problem on mixed unit interval graphs. In addition, we derive a polynomial-time algorithm for certain subclasses of mixed unit interval graphs. We point out a substantial mistake in the proof of the polynomiality of the MaxCut problem on unit interval graphs by Boyacı et al. (Inf Process Lett 121:29–33, 2017. 10.1016/j.ipl.2017.01.007). Hence, the time complexity of this problem on unit interval graphs remains open. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs.

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Some Applications of Graph Theory

Cited by 4 publications

References 124 publications

Measuring the Attractiveness of Cities to Receive Investments in Regional Airport Infrastructure

Measuring the Attractiveness of Cities to Receive Investments in Regional Airport Infrastructure

Characterization and Recognition of Proper Tagged Probe Interval Graphs

$${\mathcal {U}}$$-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

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