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Algorithms
Special Issues
Algorithms for Graphs and Networks
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Algorithms for Graphs and 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: closed (15 October 2020) | Viewed by 18363

Special Issue Editor

Dr. Rhyd Lewis

E-Mail Website
Guest Editor
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Interests: combinatorial optimisation; metaheuristics; algorithmics; operational research

Special Issue Information

Networks and graphs are structures made up of objects in which some pairs of objects are in some sense "related" to one other. Graphs are used in a surprisingly large number of problem areas including social networking, chemistry, scheduling, vehicle routing, electrical engineering, and computer networking. This Special Issue will present recent advances in the area of graphs and networks, focusing particularly on optimisation problems in graphs and algorithms and heuristics for tackling them.

We cordially invite you to submit high-quality papers to this Special Issue of Algorithms. We welcome articles presenting original research and those surveying recent advances in the area. Typical areas of interest include (but are not limited to):

  • Algorithm analysis (theoretical and empirical)
  • Problem complexity, bounds, and approximation ratios
  • Heuristics, metaheuristics, and math-heuristics
  • Graph colouring and partitioning
  • Shortest path problems
  • Methods and measures of clustering
  • Centrality measures
  • Matchings, flows, cuts and spanning trees
  • Graph classification and visualisation
  • Cycle and path identification
  • Data structures
  • Linear and integer programming with graphs
  • Vertex and arc routing problems
  • Vehicle routing problems
  • Scheduling and timetabling
  • Puzzles and games
  • Social networks and communications
  • Applications to searching in massive graphs.

If you are interested in submitting a paper on a topic other than those listed above, please contact the guest editor, Rhyd Lewis, by email and give a brief overview of your paper proposal.

Dr. Rhyd Lewis
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 submissions that pass pre-check are 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 1600 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.

Published Papers (6 papers)

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Editorial

Jump to: Research, Review

2 pages, 141 KiB  
Editorial
Editorial for the Special Issue on “Algorithms for Graphs and Networks”
by Rhyd Lewis
Algorithms 2020, 13(11), 292; https://doi.org/10.3390/a13110292 - 11 Nov 2020
Cited by 1 | Viewed by 1702
Abstract
This Special Issue of Algorithms presents recent advances in the area of graphs and networks, focusing particularly on optimisation problems and their associated algorithms [...] Full article
(This article belongs to the Special Issue Algorithms for Graphs and Networks)

Research

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21 pages, 1225 KiB  
Article
Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties
by Rhyd Lewis
Algorithms 2020, 13(11), 269; https://doi.org/10.3390/a13110269 - 22 Oct 2020
Cited by 16 | Viewed by 4281
Abstract
In this paper we review many of the well-known algorithms for solving the shortest path problem in edge-weighted graphs. We then focus on a variant of this problem in which additional penalties are incurred at the vertices. These penalties can be used to [...] Read more.
In this paper we review many of the well-known algorithms for solving the shortest path problem in edge-weighted graphs. We then focus on a variant of this problem in which additional penalties are incurred at the vertices. These penalties can be used to model things like waiting times at road junctions and delays due to transfers in public transport. The usual way of handling such penalties is through graph expansion. As an alternative, we propose two variants of Dijkstra’s algorithm that operate on the original, unexpanded graph. Analyses are then presented to gauge the relative advantages and disadvantages of these methods. Asymptotically, compared to using Dijkstra’s algorithm on expanded graphs, our first variant is faster for very sparse graphs but slower with dense graphs. In contrast, the second variant features identical worst-case run times. Full article
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
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31 pages, 2431 KiB  
Article
Solution Merging in Matheuristics for Resource Constrained Job Scheduling
by Dhananjay Thiruvady, Christian Blum and Andreas T. Ernst
Algorithms 2020, 13(10), 256; https://doi.org/10.3390/a13100256 - 09 Oct 2020
Cited by 12 | Viewed by 3274
Abstract
Matheuristics have been gaining in popularity for solving combinatorial optimisation problems in recent years. This new class of hybrid method combines elements of both mathematical programming for intensification and metaheuristic searches for diversification. A recent approach in this direction has been to build [...] Read more.
Matheuristics have been gaining in popularity for solving combinatorial optimisation problems in recent years. This new class of hybrid method combines elements of both mathematical programming for intensification and metaheuristic searches for diversification. A recent approach in this direction has been to build a neighbourhood for integer programs by merging information from several heuristic solutions, namely construct, solve, merge and adapt (CMSA). In this study, we investigate this method alongside a closely related novel approach—merge search (MS). Both methods rely on a population of solutions, and for the purposes of this study, we examine two options: (a) a constructive heuristic and (b) ant colony optimisation (ACO); that is, a method based on learning. These methods are also implemented in a parallel framework using multi-core shared memory, which leads to improving the overall efficiency. Using a resource constrained job scheduling problem as a test case, different aspects of the algorithms are investigated. We find that both methods, using ACO, are competitive with current state-of-the-art methods, outperforming them for a range of problems. Regarding MS and CMSA, the former seems more effective on medium-sized problems, whereas the latter performs better on large problems. Full article
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
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12 pages, 247 KiB  
Article
The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm
by Derek H. Smith, Roberto Montemanni and Stephanie Perkins
Algorithms 2020, 13(10), 253; https://doi.org/10.3390/a13100253 - 04 Oct 2020
Cited by 7 | Viewed by 2636
Abstract
Let G=(V,E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A [...] Read more.
Let G=(V,E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances. Full article
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
15 pages, 364 KiB  
Article
Optimization Algorithms for Detection of Social Interactions
by Vincenzo Cutello, Georgia Fargetta, Mario Pavone and Rocco A. Scollo
Algorithms 2020, 13(6), 139; https://doi.org/10.3390/a13060139 - 11 Jun 2020
Cited by 8 | Viewed by 3357
Abstract
Community detection is one of the most challenging and interesting problems in many research areas. Being able to detect highly linked communities in a network can lead to many benefits, such as understanding relationships between entities or interactions between biological genes, for instance. [...] Read more.
Community detection is one of the most challenging and interesting problems in many research areas. Being able to detect highly linked communities in a network can lead to many benefits, such as understanding relationships between entities or interactions between biological genes, for instance. Two different immunological algorithms have been designed for this problem, called Opt-IA and Hybrid-IA, respectively. The main difference between the two algorithms is the search strategy and related immunological operators developed: the first carries out a random search together with purely stochastic operators; the last one is instead based on a deterministic Local Search that tries to refine and improve the current solutions discovered. The robustness of Opt-IA and Hybrid-IA has been assessed on several real social networks. These same networks have also been considered for comparing both algorithms with other seven different metaheuristics and the well-known greedy optimization Louvain algorithm. The experimental analysis conducted proves that Opt-IA and Hybrid-IA are reliable optimization methods for community detection, outperforming all compared algorithms. Full article
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
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Review

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19 pages, 479 KiB  
Review
Multi-objective Beam-ACO for Maximising Reliability and Minimising Communication Overhead in the Component Deployment Problem
by Dhananjay Thiruvady, Asef Nazari and Aldeida Aleti
Algorithms 2020, 13(10), 252; https://doi.org/10.3390/a13100252 - 03 Oct 2020
Cited by 3 | Viewed by 2201
Abstract
Automated deployment of software components into hardware resources is a highly constrained optimisation problem. Hardware memory limits which components can be deployed into the particular hardware unit. Interacting software components have to be deployed either into the same hardware unit, or connected units. [...] Read more.
Automated deployment of software components into hardware resources is a highly constrained optimisation problem. Hardware memory limits which components can be deployed into the particular hardware unit. Interacting software components have to be deployed either into the same hardware unit, or connected units. Safety concerns could restrict the deployment of two software components into the same unit. All these constraints hinder the search for high quality solutions that optimise quality attributes, such as reliability and communication overhead. When the optimisation problem is multi-objective, as it is the case when considering reliability and communication overhead, existing methods often fail to produce feasible results. Moreover, this problem can be modelled by bipartite graphs with complicating constraints, but known methods do not scale well under the additional restrictions. In this paper, we develop a novel multi-objective Beam search and ant colony optimisation (Beam-ACO) hybrid method, which uses problem specific bounds derived from communication, co-localisation and memory constraints, to guide the search towards feasibility. We conduct an experimental evaluation on a range of component deployment problem instances with varying levels of difficulty. We find that Beam-ACO guided by the co-localisation constraint is most effective in finding high quality feasible solutions. Full article
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
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