Abstract: This study focuses on the problem of handoff minimization for a set of users moving in a wireless network. This problem is analyzed by considering two cases for the user's movement under access point capacity constraints:1) all users move together, and 2) each user can have their chosen path within the network. In the first case, we propose an optimal competitive ratio algorithm for the problem. However, in the second case, having the connectivity assumption, that is, "if a user is connected to an access point so long that the received signal strength of the access point is not less than a specified threshold, the user should continue his/her connection", we prove that no approach can reduce the number of unnecessary handoffs in an offline setting. However, without connectivity assumption, we present an optimal deterministic algorithm with the competitive ratio of nΔ for this problem under online setting, where n is the number of users and Δ is the maximum number of access points which cover any single point in the environment. Also, we prove that the randomized version of the algorithm achieves an expected competitive ratio of O(log Δ).