The Optimal Design of Low-Latency Virtual Backbones

Validi, Hamidreza; Buchanan, Austin

doi:10.1287/ijoc.2019.0914

Cited by 5 publications

(2 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existing studies focus on the probability of an edge being used in a uniformly sampled spanning tree (Teixeira et al, 2013;Hayashi et al, 2016). Identifying "central" trees could serve in application as developing communication protocols; their relationships to connected dominating sets (Guha and Khuller, 1998;Validi and Buchanan, 2020) could also be further investigated.…”

Section: Future Workmentioning

confidence: 99%

The Star Degree Centrality Problem: A Decomposition Approach

Camur

Sharkey

Vogiatzis

2022

INFORMS Journal on Computing

View full text Add to dashboard Cite

We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, is shown to be [Formula: see text]-complete. In this work, we first propose a new integer programming (IP) formulation, which has a smaller number of constraints and nonzero coefficients in them than the existing formulation in the literature. We present classes of networks in which the problem is solvable in polynomial time and offer a new proof of [Formula: see text]-completeness that shows the problem remains [Formula: see text]-complete for both bipartite and split graphs. In addition, we propose a decomposition framework that is suitable for both the existing and our formulations. We implement several acceleration techniques in this framework, motivated by techniques used in Benders decomposition. We test our approaches on networks generated based on the Barabási–Albert, Erdös–Rényi, and Watts–Strogatz models. Our decomposition approach outperforms solving the IP formulations in most of the instances in terms of both solution time and quality; this is especially true for larger and denser graphs. We then test the decomposition algorithm on large-scale protein–protein interaction networks, for which SDC is shown to be an important centrality metric. Summary of Contribution: In this study, we first introduce a new integer programming (NIP) formulation for the star degree centrality (SDC) problem in which the goal is to identify the induced star with the largest open neighborhood. We then show that, although the SDC can be efficiently solved in tree graphs, it remains [Formula: see text]-complete in both split and bipartite graphs via a reduction performed from the set cover problem. In addition, we implement a decomposition algorithm motivated by Benders decomposition together with several acceleration techniques to both the NIP formulation and the existing formulation in the literature. Our experimental results indicate that the decomposition implementation on the NIP is the best solution method in terms of both solution time and quality.

show abstract

Section: Future Workmentioning

confidence: 99%

The Star Degree Centrality Problem: A Decomposition Approach

Camur

Sharkey

Vogiatzis

2022

INFORMS Journal on Computing

View full text Add to dashboard Cite

show abstract

“…We describe this equivalence in Section 4.1, where we also present the classical protocol for the forest polytope of general graphs [12]. In Section 4.2, we 1 See [15,30] for a correction to Williams' proof. 2 A graph H is a minor of a graph G if H is isomorphic to a graph obtained from a subgraph of G by contracting edges.…”

Section: Introductionmentioning

confidence: 99%

Smaller extended formulations for spanning tree polytopes in minor-closed classes and beyond

Aprile,

Fiorini,

Huynh

et al. 2021

Preprint

View full text Add to dashboard Cite

Let G be a connected n-vertex graph in a proper minor-closed class G. We prove that the extension complexity of the spanning tree polytope of G is O(n 3/2 ). This improves on the O(n 2 ) bounds following from the work of Wong (1980) andMartin (1991). It also extends a result of Fiorini, Huynh, Joret, and Pashkovich (2017), who obtained a O(n 3/2 ) bound for graphs embedded in a fixed surface. Our proof works more generally for all graph classes admitting strongly sublinear balanced separators: We prove that for every constant β with 0 < β < 1, if G is a graph class closed under induced subgraphs such that all n-vertex graphs in G have balanced separators of size O(n β ), then the extension complexity of the spanning tree polytope of every connected n-vertex graph in G is O(n 1+β ). We in fact give two proofs of this result, one is a direct construction of the extended formulation, the other is via communication protocols. Using the latter approach we also give a short proof of the O(n) bound for planar graphs due to Williams (2002).

show abstract

Parsimonious formulations for low-diameter clusters

Salemi

Buchanan

2020

Math. Prog. Comp.

View full text Add to dashboard Cite

The Optimal Design of Low-Latency Virtual Backbones

Cited by 5 publications

References 43 publications

The Star Degree Centrality Problem: A Decomposition Approach

The Star Degree Centrality Problem: A Decomposition Approach

Smaller extended formulations for spanning tree polytopes in minor-closed classes and beyond

Parsimonious formulations for low-diameter clusters

Contact Info

Product

Resources

About