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This paper presents a general time synchronization algorithm that analyzes the time offset between any two computers clocks in a network and its evolution, by using mathematical topology properties. It builds a conversion function that produces precise and guaranteed bounds for each time conversion, and which provides accurate time synchronization. It is able to automatically adjust the observation process so as to maintain the error bound within some specified limit. It does not require adjustments to local clocks, and it features a way of filtering observation data based on a criterion of usefulness to improve precision, thus discarding only useless information. Advantages over approaches using other tools to filter out and analyze observation data (mean and variance, linear regression, midpoint functions, etc.) are exposed. Special attention is given to assessing the uncertainties and errors made in the observation …