This paper presents energy-efficient routing algorithms for wireless ad-hoc networks, aiming to maximize the network lifetime by balancing energy consumption across nodes. The authors consider a network of static wireless nodes that generate information and need to forward it to designated gateway nodes. Each node has limited battery energy, and the goal is to select routes and power levels that maximize the time until the batteries drain. The problem is formulated as a linear programming problem, where the objective is to maximize the system lifetime, defined as the minimum battery life among all nodes. The authors propose flow augmentation (FA) and flow redirection (FR) algorithms that use the shortest cost path to balance energy consumption. These algorithms are local and suitable for distributed implementation. When there is a single power level, the problem reduces to a maximum flow problem with node capacities. With multiple power levels, the achievable lifetime is close to the optimal solution. The key insight is that energy should be balanced among nodes based on their energy reserves, rather than minimizing absolute power consumption. The FA algorithm uses a link cost function that considers energy expenditure, initial energy, and residual energy. The parameters of the cost function are adjusted to optimize the system lifetime. The FR algorithm redirects flow to improve the minimum lifetime of paths, ensuring that no node's battery life is overly drained. Simulation results show that the proposed algorithms outperform conventional minimum energy routing methods, achieving up to 60% improvement in system lifetime. The algorithms perform well in both single and multicommodity cases, with FA(1,50,50) achieving near-optimal performance in most scenarios. The results demonstrate that balancing energy consumption across nodes is crucial for maximizing network lifetime in wireless ad-hoc networks.This paper presents energy-efficient routing algorithms for wireless ad-hoc networks, aiming to maximize the network lifetime by balancing energy consumption across nodes. The authors consider a network of static wireless nodes that generate information and need to forward it to designated gateway nodes. Each node has limited battery energy, and the goal is to select routes and power levels that maximize the time until the batteries drain. The problem is formulated as a linear programming problem, where the objective is to maximize the system lifetime, defined as the minimum battery life among all nodes. The authors propose flow augmentation (FA) and flow redirection (FR) algorithms that use the shortest cost path to balance energy consumption. These algorithms are local and suitable for distributed implementation. When there is a single power level, the problem reduces to a maximum flow problem with node capacities. With multiple power levels, the achievable lifetime is close to the optimal solution. The key insight is that energy should be balanced among nodes based on their energy reserves, rather than minimizing absolute power consumption. The FA algorithm uses a link cost function that considers energy expenditure, initial energy, and residual energy. The parameters of the cost function are adjusted to optimize the system lifetime. The FR algorithm redirects flow to improve the minimum lifetime of paths, ensuring that no node's battery life is overly drained. Simulation results show that the proposed algorithms outperform conventional minimum energy routing methods, achieving up to 60% improvement in system lifetime. The algorithms perform well in both single and multicommodity cases, with FA(1,50,50) achieving near-optimal performance in most scenarios. The results demonstrate that balancing energy consumption across nodes is crucial for maximizing network lifetime in wireless ad-hoc networks.