This article tackles the problem of efficient construction of iCPI trees, frequently used in co-location pattern discovery in spatial databases. It discusses the methods for parallelization of iCPI-tree construction and plane-sweep algorithms used in state-of-the-art algorithms for co-location pattern mining. The main contribution of this paper is threefold: (1) a general algorithm for parallel iCPI-tree construction is presented, (2) two variants of parallel plane-sweep algorithm (which can be used in conjunction with the aforementioned iCPI-tree construction algorithm) are introduced and (3) all three algorithms are implemented on CUDA GPU platform and their performance is tested against an efficient multithreaded parallel implementation of iCPI-tree construction on CPU. Experiments prove that our solutions allow for large speedups over CPU version of the algorithm. This paper is an extension of the conference paper (Andrzejewski & Boinski, 2014).