Abstract: Semantic parsing has long been a fundamental problem in natural language processing. Recently, cross-domain context-dependent semantic parsing has become a new focus of research. Central to the problem is the challenge of leveraging contextual information of both natural language queries and database schemas in the interaction history. In this paper, we present a dynamic graph framework that is capable of effectively modelling contextual utterances, tokens, database schemas, and their complicated interaction as the conversation proceeds. The framework employs a dynamic memory decay mechanism that incorporates inductive bias to integrate enriched contextual relation representation, which is further enhanced with a powerful reranking model. At the time of writing, we demonstrate that the proposed framework outperforms all existing models by large margins, achieving new state-of-the-art performance on two large-scale benchmarks, the SParC and CoSQL datasets. Specifically, the model attains a 55.8% question-match and 30.8% interaction-match accuracy on SParC, and a 46.8% question-match and 17.0% interaction-match accuracy on CoSQL.