Abstract: In message passing systems for distributed memory parallel computing, the routes of message passing in many broadcasts are transparent to programmers, and the programmers can not change the routes of message passing. However, the status of application runtimes is rather complicated. It will help to improve the efficiency of broadcasts for programmers to choose the routes of message passing according to computing environment and application characteristics. Message tags are used to distinguish messages in communications so that a receiving process can receive messages correctly. Nevertheless, message tags are prone to cause applications errors. Furthermore, message tags add complexity of programming. In this paper, the formal definitions of a general logic topology structure and its fundamental features are givern firstly, and then an algorithm of broadcasts without message tags is proposed based on the general logic topology structure. Here topology structures are a kind of mechanisms which determin how the messages in a distributed operation are sent. Since the general logic topology structure is abstract, the algorithm is in fact an algorithmic framework for broadcasts without message tags. Therefore, this provides a new possible approach to solving the above problems.