Graph-based methods are popular in dependency parsing for decades. Recently, citet{yang2021headed} propose a headed span-based method. Both of them score all possible trees and globally find the highest-scoring tree. In this paper, we combine these two kinds of methods, designing several dynamic programming algorithms for joint inference. Experiments show the effectiveness of our proposed methodsfootnote{Our code is publicly available at url{https://github.com/sustcsonglin/span-based-dependency-parsing}.}.