We study the scheduling of computational tasks on one local processor and one remote processor with communication delay. This problem has important application in cloud computing. Although the communication time to transmit a task can be inferred from the known data size of the task and the transmission bandwidth, the processing time of the task is generally unknown until it is processed to completion. Given a set of independent tasks with unknown processing times, our objective is to minimize makespan. We study the problem under two scenarios: 1) the communication times of the tasks to the remote processor are smaller than their corresponding processing times on the remote processor, and 2) the communication times of the tasks to the remote processor are larger than their corresponding processing times on the remote processor. For the first scenario we propose the Semi-online Partitioning and Communication (SPaC) algorithm, and for the second scenario we propose the SPaC-Restart (SPaC-R) algorithm. Even though the offline version of this problem, with a priori known processing times, is NP-hard, we show that the proposed semionline algorithms achieve O(1) competitive ratios for their intended scenarios. We also provide competitive ratios for both algorithms for more general communication times. We use simulation to demonstrate that SPaC and SPaC-R outperform online list scheduling and performs comparably well with the best known offline heuristics.