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This setting has sparked an interest in solutions that use a runtime model which reflects the system state and operational context to monitor and adapt the system in reaction to changes during its runtime. Few solutions focus on the evolution of the model over time, i.e., its history, although history is required for monitoring temporal behaviors and may enable more informed decision-making. One reason is that handling the history of a runtime model poses an important technical challenge, as it requires tracing a part of the model over multiple model snapshots in a timely manner. Additionally, the runtime setting calls for memory-efficient measures to store and check these snapshots. Following the common practice of representing a runtime model as a typed attributed graph, we introduce a language which supports the formulation of temporal graph queries, i.e., queries on the ordering and timing in which structural changes in the history of a runtime model occurred. We present a querying scheme for the execution of temporal graph queries over history-aware runtime models. Features such as temporal logic operators in queries, the incremental execution, the option to discard history that is no longer relevant to queries, and the in-memory storage of the model, distinguish our scheme from relevant solutions. By incorporating temporal operators, temporal graph queries can be used for runtime monitoring of temporal logic formulas. Building on this capability, we present an implementation of the scheme that is evaluated for runtime querying, monitoring, and adaptation scenarios from two application domains.<\/jats:p>","DOI":"10.1007\/s10270-021-00950-6","type":"journal-article","created":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T16:03:50Z","timestamp":1640016230000},"page":"1789-1829","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Incremental execution of temporal graph queries over runtime models with history and its applications"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6971-1589","authenticated-orcid":false,"given":"Lucas","family":"Sakizloglou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0697-9195","authenticated-orcid":false,"given":"Sona","family":"Ghahremani","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1138-2425","authenticated-orcid":false,"given":"Matthias","family":"Barkowsky","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4723-730X","authenticated-orcid":false,"given":"Holger","family":"Giese","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,20]]},"reference":[{"issue":"3","key":"950_CR1","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/BF01782772","volume":"2","author":"B Alpern","year":"1987","unstructured":"Alpern, B., Schneider, F.B.: Recognizing safety and liveness. 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