A novel community detection algorithm based on local similarity of clustering coefficient in social networks

X Pan, G Xu, B Wang, T Zhang - IEEE Access, 2019 - ieeexplore.ieee.org
Community structures are integral and independent parts in a network. Community detection
plays an important role in social networks for understanding the structure and predicting …

[HTML][HTML] Strong SDP based bounds on the cutwidth of a graph

E Gaar, D Puges, A Wiegele - Computers & Operations Research, 2024 - Elsevier
Given a linear ordering of the vertices of a graph, the cutwidth of a vertex v with respect to
this ordering is the number of edges from any vertex before v (including v) to any vertex after …

A computational study of exact subgraph based SDP bounds for Max-Cut, stable set and coloring

E Gaar, F Rendl - Mathematical Programming, 2020 - Springer
The “exact subgraph” approach was recently introduced as a hierarchical scheme to get
increasingly tight semidefinite programming relaxations of several NP-hard graph …

An SDP-based approach for computing the stability number of a graph

E Gaar, M Siebenhofer, A Wiegele - Mathematical Methods of Operations …, 2022 - Springer
Finding the stability number of a graph, ie, the maximum number of vertices of which no two
are adjacent, is a well known NP-hard combinatorial optimization problem. Since this …

A bundle approach for SDPs with exact subgraph constraints

E Gaar, F Rendl - … : 20th International Conference, IPCO 2019, Ann Arbor …, 2019 - Springer
The 'exact subgraph'approach was recently introduced as a hierarchical scheme to get
increasingly tight semidefinite programming relaxations of several NP-hard graph …

[PDF][PDF] Efficient implementation of sdp relaxations for the stable set problem

E Gaar - 2018 - netlibrary.aau.at
The stable set problem is among the most prominent problems of combinatorial optimization.
Given a graph, it asks for maximum stable set, that is a set of vertices such that no two …

The exact subgraph hierarchy and its local variant for the stable set problem for Paley graphs

E Gaar, D Pucher - arXiv preprint arXiv:2412.12958, 2024 - arxiv.org
The stability number of a graph, defined as the cardinality of the largest set of pairwise non-
adjacent vertices, is NP-hard to compute. The exact subgraph hierarchy (ESH) provides a …

Partial lasserre relaxation for sparse Max-Cut

JS Campos, R Misener, P Parpas - Optimization and Engineering, 2023 - Springer
A common approach to solve or find bounds of polynomial optimization problems like Max-
Cut is to use the first level of the Lasserre hierarchy. Higher levels of the Lasserre hierarchy …

Stable-Set and Coloring bounds based on 0-1 quadratic optimization

D Pucher, F Rendl - arXiv preprint arXiv:2211.13147, 2022 - arxiv.org
We consider semidefinite relaxations of Stable-Set and Coloring, which are based on
quadratic 0-1 optimization. Information about the stability number and the chromatic number …

On semidefinite lift-and-project of combinatorial optimization problems

F Battista - 2023 - iris.uniroma1.it
Finding the stability and the chromatic number of a graph are two among the fundamental
problems in combinatorial optimization. Given a graph, the first calls for a stable set of …