An Improved Approximation for Maximum k-Dependent Set on Bipartite Graphs

10/06/2021

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by   Seyedmohammadhossein Hosseinian, et al.

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We present a (1+k/k+2)-approximation algorithm for the Maximum k-dependent Set problem on bipartite graphs for any k≥1. For a graph with n vertices and m edges, the algorithm runs in O(k m √(n)) time and improves upon the previously best-known approximation ratio of 1+k/k+1 established by Kumar et al. [Theoretical Computer Science, 526: 90–96 (2014)]. Our proof also indicates that the algorithm retains its approximation ratio when applied to the (more general) class of König-Egerváry graphs.