View is a labeled directed graph containing all information about the network that a party can learn by exchanging messages with its neighbors. View can be used to solve distributed problems on an anonymous network (i.e., a network that does not guarantee that every party has a unique identifier). This paper presents an algorithm that constructs views in a compressed form on an anonymous n-party network of any topology in at most 2n rounds with O(n6log n) bit complexity, where the time complexity (i.e., the number of local computation steps per party) is O(n6log n). This is the first view-construction algorithm that runs in O(n) rounds with polynomial bits complexity. The paper also gives an algorithm that counts the number of nonisomorphic views in the network in O(n6log n) time complexity if a view is given in the compressed form. These algorithms imply that some well-studied problems, including the leader election problem, can deterministically be solved in O(n) rounds with polynomial bit and time complexity on an anonymous n-party network of any topology.

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