Chiang Mai Journal of Science

 In this article we consider a mobility model M = (S, D, U, L, R, V, C, O), where S is a set of sources, D a set of directions, U a set of users, L a set of user movements, R a set of source movements,  V a set of velocities of sources, C a set of source coverages, and o a set of obstacles. Particularly, we study a problem called Multi-Sources Simultaneous Communication Problem (MSSCP) in this model. This problem is stated as follows: given a mobility model M = (S, D, U, L, R, V, C, O), k pairs of distinct sources {s₁, s'₁}, {s₂, s'₂},..., {s_k, s'_k}, and a time t e N, can all k pairs of sources simultaneously communicate throughout the duration t of the model without sharing a source? We show that the complexity of this problem is at least as hard as the One-In-Three 3-Satisfiability unless P=NP. In addition, we also give an exact algorithm and a heuristic one for MSSCP and show that if the communication among sources in MSSCP can be represented by a complete bipartite graph, K_m,n, then MSSCP can be solved in polynomial time.