Foremost Walks and Paths in Interval Temporal Graphs

The min-wait foremost, min-hop foremost and min-cost foremost paths and walks problems in interval temporal graphs are considered. We prove that finding min-wait foremost and min-cost foremost walks and paths in interval temporal graphs is NP-hard. We develop a polynomial time algorithm for the single-source all-destinations min-hop foremost paths problem and a pseudopolynomial time algorithm for the single-source all-destinations min-wait foremost walks problem in interval temporal graphs. We benchmark our algorithms against algorithms presented by Bentert et al. for contact sequence graphs and show, experimentally, that our algorithms perform up to 207.5 times faster for finding min-hop foremost paths and up to 23.3 times faster for finding min-wait foremost walks.