Conformance checking techniques let us find out to what degree a process\nmodel and real execution data correspond to each other. In recent years,\nalignments have proven extremely useful in calculating conformance statistics.\nMost techniques to compute alignments provide an exact solution. However, in\nmany applications, it is enough to have an approximation of the conformance\nvalue. Specifically, for large event data, the computing time for alignments is\nconsiderably long using current techniques which makes them inapplicable in\nreality. Also, it is no longer feasible to use standard hardware for complex\nprocesses. Hence, we need techniques that enable us to obtain fast, and at the\nsame time, accurate approximation of the conformance values. This paper\nproposes new approximation techniques to compute approximated conformance\nchecking values close to exact solution values in a faster time. Those methods\nalso provide upper and lower bounds for the approximated alignment value. Our\nexperiments on real event data show that it is possible to improve the\nperformance of conformance checking by using the proposed methods compared to\nusing the state-of-the-art alignment approximation technique. Results show that\nin most of the cases, we provide tight bounds, accurate approximated alignment\nvalues, and similar deviation statistics.\n