Analysis of Minimum Interaction Time for Continuous Distributed Interactive Computing

Abstract

Distributed interactive computing allows participants at different locations to interact with each other in real time. In this paper, we study the interaction times of continuous Distributed Interactive Applications (DIAs) in which the application states change due to not only user-initiated operations but also time passing. Given the clients and servers of a continuous DIA, its interaction time is directly affected by how the clients are assigned to the servers as well as the simulation time settings of the servers. We formulate the Minimum Interaction Time (MIT) problem as a combinatorial problem of these two tuning knobs and prove that it is NP-hard. We then approximate the problem by fixing the client assignment or the simulation time offsets among the servers. When the client assignment is fixed, we show that finding the minimum achievable interaction time can be reduced to a weighted bipartite matching problem. We further show that this approach establishes a tight approximation factor of 3 to the MIT problem if each client is assigned to its nearest server. When the simulation time offsets among the servers are fixed, we show that finding the minimum achievable interaction time is still NP-hard. This approach can approximate the MIT problem by a factor within 2 if the simulation times of all servers are synchronized. A mix of the above two approaches better approximates the MIT problem within a factor of 5/3. We further conduct experimental evaluation of these approaches with three real Internet latency datasets.