Parameterized Algorithms for Maximum Edge Biclique and Related Problems

Maximum Edge Biclique and related problems have wide applications in management science, bioinformatics, etc. In this paper, we study the parameterized algorithms for the Parameterized Edge Biclique problem, the Parameterized Edge Biclique Packing problem, and the Parameterized Biclique Edge Deletion problem. For the Parameterized Edge Biclique problem, the current best result is of running time \(O^*(2^k)\), and we give a parameterized algorithm of running time \(O^*({k^{\lceil \sqrt{k} \rceil }})\). For the Parameterized Edge Biclique Packing problem, based on randomized divide-and-conquer technique, a parameterized algorithm of running time \(O^*(4^{(2k-1)t)}k^{\lceil \sqrt{k} \rceil })\) is given. We study the Parameterized Biclique Edge Deletion problem on bipartite graphs and general graphs, and give parameterized algorithms of running time \(O^*(2^k)\) and \(O^*(3^k)\), respectively.