Spanning Edge Centrality

Mavroforakis, Charalampos; Garcia-Lebron, Richard; Koutis, Ioannis; Terzi, Evimaria

doi:10.1145/2736277.2741125

Cited by 32 publications

(3 citation statements)

References 21 publications

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“…Effective resistance is a pairwise metric on the vertex set of G, which results from viewing the graph as an electrical network. It relates to uniform spanning trees (Angriman et al 2020), random walks (Lovász 1996), and several centrality measures (Mavroforakis et al 2015;Brandes and Fleischer 2005). In fact, it works similarly as an objective function for k-LRIP-we are just restricted in the search space to a particular focus node.…”

Section: Introductionmentioning

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: Introductionmentioning

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.

View full text Add to dashboard Cite

show abstract

“…Effective resistance is a pairwise metric on the vertex set of G, which results from viewing the graph as an electrical network. It relates to uniform spanning trees [3], random walks [38], and several centrality measures [12,40]. In fact, it works similarly as an objective function for k-LRIP -we are just restricted in the search space to a particular focus node.…”

Section: Introductionmentioning

confidence: 99%

A k-Way Greedy Graph Partitioning with Initial Fixed Vertices for Parallel Applications

Predari

Esnard

2016

2016 24th Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP)

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Graph partitioning is used to solve the problem of distributing computations to a number of processors, in order to improve the performance of time consuming applications in parallel environments. A common approach to solve this problem is based on a multilevel framework, where the graph is firstly coarsened to a smaller instance and then it is partitioned in a number of parts using recursive bisection (RB) based methods. However, in applications where initial fixed vertices are used to model additional constraints of the problem, RB based methods often fail to produce partitions of good quality. In this paper, we propose a new direct k-way greedy graph growing algorithm, called KGGGP, that overcomes this issue and succeeds to produce partition with better quality than RB while respecting the constraint of fixed vertices. In the experimental section, we present results which compare KGGGP against state-of-theart methods for graphs available from the popular DIMACS'10 collection.

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“…Apart from the methods discussed in Section 2.3 for 𝜖-approximate PER queries, there exist several techniques for all pairwise ER computation or estimating ER values for all edges in the input graph, as reviewed in the sequel. Fouss et al[24] proposed to calculate the ER value for any node pair in the input graph 𝐺 by first computing the Moore-Penrose pseudoinverse of the Laplacian matrix D − A based on a sparse Cholesky factorization of D − A. Mavroforakis et al[42] utilized the random projection and SDD solvers to approximate the ER values of all edges. In Ref [29],.…”

mentioning

confidence: 99%

Efficient Estimation of Pairwise Effective Resistance

Yang

Tang

2023

Proc. ACM Manag. Data

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Given an undirected graph G, the effective resistance r(s,t) measures the dissimilarity of node pair s,t in G, which finds numerous applications in real-world problems, such as recommender systems, combinatorial optimization, molecular chemistry, and electric power networks. Existing techniques towards pairwise effective resistance estimation either trade approximation guarantees for practical efficiency, or vice versa. In particular, the state-of-the-art solution is based on a multitude of Monte Carlo random walks, rendering it rather inefficient in practice, especially on large graphs. Motivated by this, this paper first presents an improved Monte Carlo approach, AMC, which reduces both the length and amount of random walks required without degrading the theoretical accuracy guarantee, through careful theoretical analysis and an adaptive sampling scheme. Further, we develop a greedy approach, GEER, which combines AMC with sparse matrix-vector multiplications in an optimized and non-trivial way. GEER offers significantly improved practical efficiency over AMC without compromising its asymptotic performance and accuracy guarantees. Extensive experiments on multiple benchmark datasets reveal that GEER is orders of magnitude faster than the state of the art in terms of computational time when achieving the same accuracy.

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Spanning Edge Centrality

Cited by 32 publications

References 21 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 k-Way Greedy Graph Partitioning with Initial Fixed Vertices for Parallel Applications

Efficient Estimation of Pairwise Effective Resistance

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