Group-Harmonic and Group-Closeness Maximization – Approximation and Engineering

Angriman, Eugenio; Becker, Ruben; D’Angelo, Gianlorenzo; Gilbert, Hugo; Grinten, Alexander van der; Meyerhenke, Henning

doi:10.1137/1.9781611976472.12

Cited by 6 publications

(1 citation statement)

References 29 publications

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“…For monotonic submodular problems, the generic greedy algorithm has an approximation ratio of 1 − 1∕e . Even for non-submodular problems such as k-GRIP (see Summers et al (2017) for a counterexample), the greedy algorithm still often leads to solutions of high quality (Summers and Kamgarpour 2019; Angriman et al 2021). Stochastic greedy algorithms that improve the time complexity of the standard greedy approach (in a general setting) were proposed in Mirzasoleiman et al (2015); and Hassidim and Singer (2017).…”

Section: Related Workmentioning

confidence: 99%

Greedy optimization of resistance-based graph robustness with global and local edge insertions

Predari,

Berner,

Kooij

et al. 2023

Soc. Netw. Anal. Min.

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The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph G. We consider two optimization problems of adding k new edges to G such that the resulting graph has minimal total effective resistance (i.e., is most robust)—one where the new edges can be anywhere in the graph and one where the new edges need to be incident to a specified focus node. The total effective resistance and effective resistances between nodes can be computed using the pseudoinverse of the graph Laplacian. The pseudoinverse may be computed explicitly via pseudoinversion, yet this takes cubic time in practice and quadratic space. We instead exploit combinatorial and algebraic connections to speed up gain computations in an established generic greedy heuristic. Moreover, we leverage existing randomized techniques to boost the performance of our approaches by introducing a sub-sampling step. Our different graph- and matrix-based approaches are indeed significantly faster than the state-of-the-art greedy algorithm, while their quality remains reasonably high and is often quite close. Our experiments show that we can now process larger graphs for which the application of the state-of-the-art greedy approach was impractical before.

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Section: Related Workmentioning

confidence: 99%

Greedy optimization of resistance-based graph robustness with global and local edge insertions

Predari,

Berner,

Kooij

et al. 2023

Soc. Netw. Anal. Min.

Self Cite

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A survey on optimization studies of group centrality metrics

Camur,

Vogiatzis

2024

Networks

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Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of centrality have started attracting scientific and practitioner interest. The identification of sets of nodes that are influential within a network is becoming increasingly more important. This is even more pronounced when these sets of nodes are required to induce a certain motif or structure. In this study, we review group centrality metrics from an operations research and optimization perspective for the first time. This is particularly interesting due to the rapid evolution and development of this area in the operations research community over the last decade. We first present a historical overview of how we have reached this point in the study of group centrality. We then discuss the different structures and motifs that appear prominently in the literature, alongside the techniques and methodologies that are popular. We finally present possible avenues and directions for future work, mainly in three areas: (i) probabilistic metrics to account for randomness along with stochastic optimization techniques; (ii) structures and relaxations that have not been yet studied; and (iii) new emerging applications that can take advantage of group centrality. Our survey offers a concise review of group centrality and its intersection with network analysis and optimization.

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Algorithms for Large-Scale Network Analysis and the NetworKit Toolkit

Angriman

Grinten

Hamann

et al. 2022

Lecture Notes in Computer Science

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The abundance of massive network data in a plethora of applications makes scalable analysis algorithms and software tools necessary to generate knowledge from such data in reasonable time. Addressing scalability as well as other requirements such as good usability and a rich feature set, the open-source software NetworKit has established itself as a popular tool for large-scale network analysis. This chapter provides a brief overview of the contributions to NetworKit made by the SPP 1736. Algorithmic contributions in the areas of centrality computations, community detection, and sparsification are in the focus, but we also mention several other aspects – such as current software engineering principles of the project and ways to visualize network data within a NetworKit-based workflow.

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Group-Harmonic and Group-Closeness Maximization – Approximation and Engineering

Abstract: Centrality measures characterize important nodes in networks. Efficiently computing such nodes has received a lot of attention. When considering the generalization of computing central groups of nodes, challenging *

Cited by 6 publications

References 29 publications

Greedy optimization of resistance-based graph robustness with global and local edge insertions

Greedy optimization of resistance-based graph robustness with global and local edge insertions

A survey on optimization studies of group centrality metrics

Algorithms for Large-Scale Network Analysis and the NetworKit Toolkit

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