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Article

Multiple Hungarian Method for k-Assignment Problem

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Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia
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Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia
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Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 2050; https://doi.org/10.3390/math8112050
Received: 28 September 2020 / Revised: 13 November 2020 / Accepted: 13 November 2020 / Published: 17 November 2020
The k-assignment problem (or, the k-matching problem) on k-partite graphs is an NP-hard problem for k3. In this paper we introduce five new heuristics. Two algorithms, Bm and Cm, arise as natural improvements of Algorithm Am from (He et al., in: Graph Algorithms And Applications 2, World Scientific, 2004). The other three algorithms, Dm, Em, and Fm, incorporate randomization. Algorithm Dm can be considered as a greedy version of Bm, whereas Em and Fm are versions of local search algorithm, specialized for the k-matching problem. The algorithms are implemented in Python and are run on three datasets. On the datasets available, all the algorithms clearly outperform Algorithm Am in terms of solution quality. On the first dataset with known optimal values the average relative error ranges from 1.47% over optimum (algorithm Am) to 0.08% over optimum (algorithm Em). On the second dataset with known optimal values the average relative error ranges from 4.41% over optimum (algorithm Am) to 0.45% over optimum (algorithm Fm). Better quality of solutions demands higher computation times, thus the new algorithms provide a good compromise between quality of solutions and computation time. View Full-Text
Keywords: k-assignment problem; k-matching problem; heuristic algorithm; local search; greedy algorithm; hungarian method k-assignment problem; k-matching problem; heuristic algorithm; local search; greedy algorithm; hungarian method
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MDPI and ACS Style

Gabrovšek, B.; Novak, T.; Povh, J.; Rupnik Poklukar, D.; Žerovnik, J. Multiple Hungarian Method for k-Assignment Problem. Mathematics 2020, 8, 2050. https://doi.org/10.3390/math8112050

AMA Style

Gabrovšek B, Novak T, Povh J, Rupnik Poklukar D, Žerovnik J. Multiple Hungarian Method for k-Assignment Problem. Mathematics. 2020; 8(11):2050. https://doi.org/10.3390/math8112050

Chicago/Turabian Style

Gabrovšek, Boštjan, Tina Novak, Janez Povh, Darja Rupnik Poklukar, and Janez Žerovnik. 2020. "Multiple Hungarian Method for k-Assignment Problem" Mathematics 8, no. 11: 2050. https://doi.org/10.3390/math8112050

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