Document Type
Conference Presentation
Publication Date
2024
Abstract
In this paper, we demonstrate a deterministic algorithm that approximates the optimal path cover on various graphs and networks derived from a wide range of real world problems. Based on the 1-Approximation Path Cover Algorithm by Moran et al., we first organize the original algorithm into two versions - one with redundant edge removal and one without. To compare the two versions of algorithms, we prove the number of redundant edges for any general graphs to analyze the effects of edge removal. We also analyze theoretical guarantees of the two algorithms. To test the time complexity and performance, we conduct numerical tests on graphs with various structures and random weights, from structured ring graphs to random graphs, such as Erd˝os-R´enyi graphs. The tests demonstrate the advantage in memory saving of the algorithm that does not remove any redundant edges and time saving of the other one, especially on large and high density graphs. We also perform tests on various graphs and networks derived from a wide range ofreal-world problems to suggest the effectiveness and applicability of both algorithms.
Original Publication Citation
Lin, Junyuan, and Guangpeng Ren. Implementation of 1/2-Approximation Path Cover Algorithm and Its Empirical Analysis. 2024 HAWAII UNIVERSITY INTERNATIONAL CONFERENCES, 4 July 2024, https://huichawaii.org/lin-junyuan%c2%b9-ren-guangpeng%c2%b2/.
Digital Commons @ LMU & LLS Citation
Lin, Junyuan and Ren, Guangpen, "Implementation of 1/2-Approximation Path Cover Algorithm and Its Empirical Analysis" (2024). Mathematics, Statistics and Data Science Faculty Works. 208.
https://digitalcommons.lmu.edu/math_fac/208
