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Article

On the Embed and Project Algorithm for the Graph Bandwidth Problem

by 1,2
1
Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva ulica 6, SI-1000 Ljubljana, Slovenia
2
Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
Academic Editor: Takayuki Hibi
Mathematics 2021, 9(17), 2030; https://doi.org/10.3390/math9172030
Received: 30 July 2021 / Revised: 19 August 2021 / Accepted: 20 August 2021 / Published: 24 August 2021
(This article belongs to the Section Computational and Applied Mathematics)
The graph bandwidth problem, where one looks for a labeling of graph vertices that gives the minimum difference between the labels over all edges, is a classical NP-hard problem that has drawn a lot of attention in recent decades. In this paper, we focus on the so-called Embed and Project Algorithm (EPA) introduced by Blum et al. in 2000, which in the main part has to solve a semidefinite programming relaxation with exponentially many linear constraints. We present several theoretical properties of this special semidefinite programming problem (SDP) and a cutting-plane-like algorithm to solve it, which works very efficiently in combination with interior-point methods or with the bundle method. Extensive numerical results demonstrate that this algorithm, which has only been studied theoretically so far, in practice gives very good labeling for graphs with n1000. View Full-Text
Keywords: graph bandwidth problem; semidefinite programming; combinatorial optimization; embed and project algorithm; approximation algorithm graph bandwidth problem; semidefinite programming; combinatorial optimization; embed and project algorithm; approximation algorithm
MDPI and ACS Style

Povh, J. On the Embed and Project Algorithm for the Graph Bandwidth Problem. Mathematics 2021, 9, 2030. https://doi.org/10.3390/math9172030

AMA Style

Povh J. On the Embed and Project Algorithm for the Graph Bandwidth Problem. Mathematics. 2021; 9(17):2030. https://doi.org/10.3390/math9172030

Chicago/Turabian Style

Povh, Janez. 2021. "On the Embed and Project Algorithm for the Graph Bandwidth Problem" Mathematics 9, no. 17: 2030. https://doi.org/10.3390/math9172030

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