Assessing the Computational Complexity of Multi-layer Subgraph Detection

Bredereck, Robert; Komusiewicz, Christian; Kratsch, Stefan; Molter, Hendrik; Niedermeier, Rolf; Sorge, Manuel

doi:10.1007/978-3-319-57586-5_12

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…On the positive side, we also managed to identify a number of natural special cases which are tractable ( Table 1 summarizes our results). Interestingly, while in the world of multi-layer stable matchings the case of two layers already leads to most computational hardness results, in the world of maximum-cardinality matching in two-layer graphs one obtains polynomial-time solvability, while in the case of three layers one encounters NP-hardness [14].…”

Section: Open Problems and Conclusionmentioning

confidence: 99%

Stable Marriage with Multi-Modal Preferences

Chen

Niedermeier

Skowron

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

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We introduce a generalized version of the famous STABLE MARRIAGE problem, now based on multimodal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the GRAPH ISOMORPHISM problem.

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Section: Open Problems and Conclusionmentioning

confidence: 99%

Stable Marriage with Multi-Modal Preferences

Chen

Niedermeier

Skowron

2018

Proceedings of the 2018 ACM Conference on Economics and Computation

Self Cite

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“…It is known that the maximum bipartite matching for networks of up to two layers can be determined in polynomial time, whereas the computation of such a matching for networks of three or more layers is NP-hard 31 . This fact suggests that the minimum set of driver nodes under linear structural controllability 5 can be obtained in polynomial time only for networks of up to two layers.…”

Section: Theoretical Resultsmentioning

confidence: 99%

Finding and analysing the minimum set of driver nodes required to control multilayer networks

Nacher

Ishitsuka

Miyazaki

et al. 2019

Sci Rep

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It is difficult to control multilayer networks in situations with real-world complexity. Here, we first define the multilayer control problem in terms of the minimum dominating set (MDS) controllability framework and mathematically demonstrate that simple formulas can be used to estimate the size of the minimum dominating set in multilayer (MDSM) complex networks. Second, we develop a new algorithm that efficiently identifies the MDSM in up to 6 layers, with several thousand nodes in each layer network. Interestingly, the findings reveal that the MDSM size for similar networks does not significantly differ from that required to control a single network. This result opens future directions for controlling, for example, multiple species by identifying a common set of enzymes or proteins for drug targeting. We apply our methods to 70 genome-wide metabolic networks across major plant lineages, unveiling some relationships between controllability in multilayer networks and metabolic functions at the genome scale.

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“…In this approach data manipulation are specified as type constructors and graph-oriented operations. [4] Graph which consists of several layers with multiple relationships can be shortened by considering two or three layers and by truncating the rest. [5] For sampling large and dynamic graph, simulation was done using random graphs and snapshot of the Gnutella.…”

Section: Related Workmentioning

confidence: 99%

Sub graph sampling and case citation network: a case study

Khanam¹,

Wagh²

2018

IJET

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Graphs or networks very commonly are used to represent connected or linked data. With the penetration of www in every sphere of life networked relationships can be easily established through communication links over web and network and graph analysis come as obvious choices of data representation and analysis. There are processes which can be analysed as network not through web but through the knowledge links available in these domains. In both these cases network analysis is challenged by the enormous size of the network in terms of nodes and links. Sub graph sampling can effectively be employed on large network structures to reduce the size of data while preserving the original properties of the network. Through this paper authors present a case study on application of sub graph sampling approach to obtain reduced case citation network in legal domain.

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Assessing the Computational Complexity of Multi-layer Subgraph Detection

Cited by 7 publications

References 33 publications

Stable Marriage with Multi-Modal Preferences

Stable Marriage with Multi-Modal Preferences

Finding and analysing the minimum set of driver nodes required to control multilayer networks

Sub graph sampling and case citation network: a case study

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