A novel video object segmentation algorithm, which segments out multiple objects in a video sequence in unsupervised or weakly supervised manners, is proposed in this work. First, we match visually important object instances to construct salient object tracks through a video sequence without any user supervision. We formulate this matching process as the problem to find maximal weight cliques in a complete k-partite graph and develop the sequential clique optimization algorithm to determine the cliques efficiently. Then, we convert the resultant salient object tracks into object segmentation results and refine them based on Markov random field optimization. Second, we adapt the sequential clique optimization algorithm to perform weakly supervised video object segmentation. To this end, we develop a sparse-to-dense network to convert the point cliques into segmentation results. The experimental results demonstrate that the proposed algorithm provides comparable or better performances than recent state-of-the-art VOS algorithms.