Special Issue "Multilevel Refinement for Combinatorial Optimisation and Complex Networks"

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Combinatorial Optimization, Graph, and Network Algorithms".

Deadline for manuscript submissions: 15 April 2021.

Special Issue Editor

Dr. Chris Walshaw
Guest Editor
School of Computing and Mathematical Sciences, University of Greenwich, London, UK
Interests: combinatorial optimisation; multilevel refinement; graph partitioning; graph visualisation; music similarity

Special Issue Information

Dear Colleagues,

The multilevel approach to finding solutions for combinatorial and network problems is relatively straightforward, and at its most basic involves recursive coarsening/simplification to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes at the coarsest level) and then iteratively refined at each level, typically using local search algorithms. Projection operators can transfer the solution from one level to another.

Despite using local coarsening and refinement heuristics, the multilevel approach has the effect of filtering the solution space, often by removing most of the low-quality solutions. Typically, this allows even local search algorithms to explore a representative subset of the high-quality solutions, and many authors have reported excellent results and highly competitive implementations in a number of research areas.

As a result, since its introduction as a solution metaheuristic for the graph partitioning problem in the early 1990s, the multilevel paradigm has gone from strength to strength and has been applied to an increasingly wide range of combinatorial and network problems, including graph visualisation, the travelling salesman problem, graph clustering, image segmentation, vehicle routing, DNA sequencing, and many others. A recent survey paper by Valejo et al., “A Critical Survey of the Multilevel Method in Complex Networks”, cites over 150 papers (the most popular of which has been cited around 10,000 times) that use multilevel methods or variants.

To update these results and the multilevel research field in general, you are warmly invited to submit high-quality papers to this Special Issue on “Multilevel Refinement for Combinatorial Optimisation and Complex Networks”. Papers may cover theory and/or applications, including but not limited to:

  • Graph partitioning;
  • Graph clustering/community detection
  • Graph drawing/visualisation;
  • Combinatorial optimisation;
  • Complex networks.
  • Conceptual/experimental comparisons with related techniques such as multiscale methods, multigrid techniques or statistical multilevel modelling

Dr. Chris Walshaw
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • multilevel refinement
  • coarsening/contraction/reduction
  • graph partitioning
  • graph clustering/community detection
  • graph drawing/visualisation
  • combinatorial optimisation
  • complex networks

Published Papers

This special issue is now open for submission.
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