A family of new generalized LR parsing algorithms are proposed which make use of a set of ancestors tables introduced by Kipps. As Kipps's algorithm does not give us a method to extract any parsing results, his algorithm is not considered as a practical parser but as a recognizer. In this paper, we will propose two methods to extract all parse trees from a set of ancestors tables in the top vertices of a graph-structured stack. For an input sentence of length n, while the time complexity of the Tomita parser can exceed O(n3) for some context-free grammars (CFGs), the time complexity of our parser is O(n3) for any CFGs, since our algorithm is based on the Kipps's recognizer. In order to extract a parse tree from a set of ancestors tables, it takes time in order n2. Some preliminary experimental results are given to show the efficiency of our parsers over Tomita parser.