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We incorporate the clock skew in the message exchange mechanism, without which the clock synchronization problem remains practically unsolved. For the offset-only case, we determine the ML estimators through a simple application of convex optimization, alleviating the need for the graphical search mentioned. We also propose estimators that outperform the ML estimators in terms of MSE. For the joint estimation of clock offset and skew, we show that the likelihood maximization can be equivalently represented as a linear program and can be solved efficiently by any gradient descent method.