An arXiv version 1 preprint dated 20 Aug 2026 reports a process-discovery method for partially ordered event traces that matched all 1,000 evaluation traces perfectly at nine executions. Sequential discovery reached the same 100% coverage only around 24 executions in the controlled simulation.
Keeping unresolved order in the record
Partially ordered traces preserve known precedence while leaving some event pairs unordered, so the data do not say which came first. POT-IM computes the evidence needed for discovery directly from that structure, rather than choosing one compatible sequence or enumerating every compatible sequence.
During timestamp preprocessing, the method creates a fresh labeled event for each row in a case and infers precedence only when the timestamp gap exceeds an optional tolerance window. Equal or near-equal times can remain incomparable, so they need not be forced into an order by an ascending- or descending-label tie-break.
The cost of spelling out every sequence
To test scalability, the researchers used one partial-order trace at each concurrency width of 2, 4, 6, 8 and 10 activities. Each trace had k + 2 events and represented k! sequential executions. The comparison covered direct POT-IM, a baseline using one compatible sequence and a baseline materializing all compatible sequences.
At width 10, POT-IM took 0.008 seconds and detected concurrency. The one-sequence baseline took 0.007 seconds but did not detect it. Producing all 3,628,800 compatible cases represented 43,545,600 events, took 1,929.244 seconds to materialize, and then took 600.539 seconds for Inductive Miner discovery.
When timestamp ties change the result
For the BPI Challenge 2012 log, the comparison retained completion events, set the partial-order timestamp tolerance to zero, and created two sequential logs by ordering tied activity labels in ascending and descending order.
Without filtering, the model from Lasc fit 100% of its own traces but only 80.6% of Ldes. The model from Ldes likewise fit 100% of its own traces but only 64.8% of Lasc. POT-IM fit both logs completely, with average trace fitness of 1 on each and a precision difference of 0.004 between the two tie-breaking versions.
Applying a filtering threshold of 0.8 made the models’ fitting-trace percentages equal across the two sequential logs. The sequential model trained on Lasc then had the highest absolute fitness and precision, while POT-IM remained the least sensitive to tie-breaking.
A controlled test of data efficiency
To compare the amount of input needed by the two representations, the researchers generated 1,000 non-empty executions from a fixed partial-order reference process. Each partial-order execution was paired with a compatible sequential trace produced by random topological sorting. At every input size, the two discoveries used equal numbers of executions and were evaluated on the same full 1,000-trace sequential log.
At n = 9, POT-based discovery achieved perfect fits on all 1,000 evaluation traces and retained 100% coverage. Sequential discovery reached 100% only around n = 24, dropped around n = 27–28, and returned to 100% from n = 29.
The model-level comparison pointed the same way. POT-based discovery reached behavioral similarity of approximately 0.68 after eight observations, approximately 0.88 at n = 50 and approximately 0.91 from n = 80 onward. Sequential discovery reached roughly the initial 0.68 level only after about two dozen observations and remained near 0.68 at larger sizes.
A result tied to the test design
The sample-efficiency result came from a controlled simulation using a fixed partial-order reference process. The synthetic scalability test used one partial-order trace at each tested width.
Paper data and sources
Original title: Inductive Process Discovery from Partially Ordered Event Data
Authors: Humam Kourani, Tom Breuer, Gyunam Park, Wil M. P. van der Aalst
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
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