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Earth observation satellites (EOS) such as Landsat provide image datasets that can be immensely useful in numerous application domains. One way of analyzing satellite images for land use and land cover change (LULCC) is time series analysis (TSA). Several algorithms for time series analysis have been proposed by various groups in remote sensing; more algorithms (that can be adapted) are available in the general time series literature. However, in spite of an abundance of algorithms, the choice of algorithm to be used for analyzing an image stack is presently an open question. A concurrent issue is the prohibitive size of Landsat datasets, currently of the order of petabytes and growing. This makes them computationally unwieldy --- both in storage and processing. An EOS image stack typically consists of multiple images of a fixed area on the Earth's surface (same latitudes and longitudes) taken at different time points. Experiments on multicore servers indicate that carrying out meaningful time series analysis on one such interannual, multitemporal stack with existing state of the art codes can take several days. This work proposes using multiple algorithms to analyze a given image stack in a polyalgorithmic framework. A polyalgorithm combines several basic algorithms, each meant to solve the same problem, producing a strategy that unites the strengths and circumvents the weaknesses of constituent algorithms. The foundation of the proposed TSA based polyalgorithm is laid using three algorithms (LandTrendR, EWMACD, and BFAST). These algorithms are precisely described mathematically, and chosen to be fundamentally distinct from each other in design and in the phenomena they capture. Analysis of results representing success, failure, and parameter sensitivity for each algorithm is presented. Scalability issues, important for real simulations, are also discussed, along with scalable implementations, and speedup results. For a given pixel, Hausdorff distance is used to compare the distance between the change times (breakpoints) obtained from two different algorithms. Timesync validation data, a dataset that is based on human interpretation of Landsat time series in concert with historical aerial photography, is used for validation. The polyalgorithm yields more accurate results than EWMACD and LandTrendR alone, but counterintuitively not better than BFAST alone. This nascent work will be directly useful in land use and land cover change studies, of interest to terrestrial science research, especially regarding anthropogenic impacts on the environment, and in much broader applications such as health monitoring and urban transportation.