Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We compare two methods that calculate the sparsity pattern of Hessian matrices using the computational framework of automatic differentiation. The first method is a forward-mode algorithm by Andrea Walther in 2008 which has been implemented as the driver called hess_pat in the automatic differentiation package ADOL-C. The second is edge_push_sp, a new reverse mode algorithm descended from the edge pushing algorithm for calculating Hessians by Gower and Mello in 2012. We present complexity analysis and perform numerical tests for both algorithms. The results show that the new reverse algorithm is very promising.402Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [2009/04785-7, 2006/53768-0]