IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Special Section on Parallel and Distributed Computing and Networking
Accelerating the Held-Karp Algorithm for the Symmetric Traveling Salesman Problem
Kazuro KIMURAShinya HIGAMasao OKITAFumihiko INO
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2019 Volume E102.D Issue 12 Pages 2329-2340


In this paper, we propose an acceleration method for the Held-Karp algorithm that solves the symmetric traveling salesman problem by dynamic programming. The proposed method achieves acceleration with two techniques. First, we locate data-independent subproblems so that the subproblems can be solved in parallel. Second, we reduce the number of subproblems by a meet in the middle (MITM) technique, which computes the optimal path from both clockwise and counterclockwise directions. We show theoretical analysis on the impact of MITM in terms of the time and space complexities. In experiments, we compared the proposed method with a previous method running on a single-core CPU. Experimental results show that the proposed method on an 8-core CPU was 9.5-10.5 times faster than the previous method on a single-core CPU. Moreover, the proposed method on a graphics processing unit (GPU) was 30-40 times faster than that on an 8-core CPU. As a side effect, the proposed method reduced the memory usage by 48%.

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© 2019 The Institute of Electronics, Information and Communication Engineers
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