Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest.However,in certain applications,barrier coverage cannot be satisfied after random deployment.In this paper,we study how mobile sensors can be efficiently relocated to achieve k-barrier coverage.In particular,two problems are studied:relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost.These two problems were formulated as 0–1 integer linear programming(ILP).The formulation is computationally intractable because of integrality and complicated constraints.Therefore,we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0–1 ILP rapidly through linear programming.Theoretical analysis and simulation were performed to verify the effectiveness of our approach. Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest. Home, in certain applications, barrier coverage can not be satisfied after random deployment. In this paper, we study how mobile sensors can two of them are studied: relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost. two of these problems were formulated as 0-1 integer linear programming (ILP). The formulation is computationally intractable because of integrality and complicated constraints.Therefore, we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0-1 ILP rapidly through linear programming. Theoretical analysis and simulation were performed to verify the effecti veness of our approach.