We present initial results from the low-latitude Galactic plane region of the High Time Resolution Universe pulsar survey conducted at the Parkes 64-m radio telescope. We discuss the computational challenges arising from the processing of the terabyte-sized survey data. Two new radio interference mitigation techniques are introduced, as well as a partially-coherent segmented acceleration search algorithm which aims to increase our chances of discovering highly-relativistic short-orbit binary systems, covering a parameter space including potential pulsar-black hole binaries. We show that under a constant acceleration approximation, a ratio of data length over orbital period of ~0.1 results in the highest effectiveness for this search algorithm. From the 50 per cent of data processed thus far, we have re-detected 435 previously known pulsars and discovered a further 60 pulsars, two of which are fast-spinning pulsars with periods less than 30ms. PSR J1101-6424 is a millisecond pulsar whose heavy white dwarf (WD) companion and short spin period of 5.1ms indicate a rare example of full-recycling via Case A Roche lobe overflow. PSR J1757-27 appears to be an isolated recycled pulsar with a relatively long spin period of 17ms. In addition, PSR J1244-6359 is a mildly-recycled binary system with a heavy WD companion, PSR J1755-25 has a significant orbital eccentricity of 0.09, and PSR J1759-24 is likely to be a long-orbit eclipsing binary with orbital period of the order of tens of years. Comparison of our newly-discovered pulsar sample to the known population suggests that they belong to an older population. Furthermore, we demonstrate that our current pulsar detection yield is as expected from population synthesis.
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