Algorithms for Hard Graph Problems

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Randomized, Online, and Approximation Algorithms".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 3744

Special Issue Editor


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Guest Editor
Institute of Computer Science, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
Interests: graph theory; graph algorithms; parameterized complexity; combinatorial optimization

Special Issue Information

Dear Colleagues,

Graphs have been used for a long time in many different areas of engineering and science. Since many interesting problems on graphs are hard, several approaches for solving hard problems have been applied to these problems. These include parameterized algorithms, exponential time algorithms, approximation algorithms, randomized algorithms, heuristic algorithms, and algorithms for special graph classes. For this Special Issue on “Algorithms for Hard Graph Problems”, we welcome papers presenting original research concerned with all fields of solving hard graph problems. Works on undirected graphs as well as works on directed graphs are welcome.

Dr. Frank Gurski
Guest Editor

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Keywords

  • parameterized algorithms
  • exponential time algorithms
  • approximation algorithms
  • randomized algorithms
  • heuristic algorithms
  • algorithms for special graph classes
  • width parameters

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Published Papers (1 paper)

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Research

12 pages, 325 KiB  
Article
A Performance Study of Some Approximation Algorithms for Computing a Small Dominating Set in a Graph
by Jonathan Li, Rohan Potru and Farhad Shahrokhi
Algorithms 2020, 13(12), 339; https://doi.org/10.3390/a13120339 - 14 Dec 2020
Cited by 6 | Viewed by 3081
Abstract
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the [...] Read more.
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the greedy and LP rounding algorithms. Over the range of test data, all algorithms perform better than anticipated in theory, and have small performance ratios, measured as the size of output divided by the LP objective lower bound. However, each have advantages over the others. For instance, LP rounding algorithm normally outperforms the other algorithms on sparse real-world graphs. On a graph with 400,000+ vertices, LP rounding took less than 15 s of CPU time to generate a solution with performance ratio 1.011, while the greedy and hybrid algorithms generated solutions of performance ratio 1.12 in similar time. For synthetic graphs, the hybrid algorithm normally outperforms the others, whereas for hypercubes and k-Queens graphs, greedy outperforms the rest. Another advantage of the hybrid algorithm is to solve very large problems that are suitable for application of LP rounding (sparse graphs) but LP formulations become formidable in practice and LP solvers crash, as we observed on a real-world graph with 7.7 million+ vertices and a planar graph on 1,000,000 vertices. Full article
(This article belongs to the Special Issue Algorithms for Hard Graph Problems)
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