No abstract

The pebble motion on trees (PMT) problem consists in finding a feasible sequence of moves that repositions a set of pebbles to assigned target vertices. This problem has been widely studied because, in many cases, the more general Multi-Agent path finding (MAPF) problem on graphs can be reduced to PMT. We propose a simple and easy to implement procedure, which finds solutions of length O(knc + n 2 ), where n is the number of nodes, k is the number of pebbles, and c the maximum length of corridors in the tree. This complexity result is more detailed than the current best known result O(n 3 ), which is equal to our result in the worst case, but does not capture the dependency on c and k.

Introduction: Radiological response assessment to immune checkpoint inhibitor is challenging due to atypical pattern of response and commonly used RECIST 1.1 criteria do not take into account the kinetics of tumor behavior. Our study aimed at evaluating the tumor growth rate (TGR) in addition to RECIST 1.1 criteria to assess the benefit of immune checkpoint inhibitors (ICIs). Methods: Tumor real volume was calculated with a dedicated computed tomography (CT) software that semi-automatically assess tumor volume. Target lesions were identified according to RECIST 1.1. For each patient, we had 3 measurement of tumor volume. CT-1 was performed 8–12 weeks before ICI start, the CT at baseline for ICI was CT0, while CT + 1 was the first assessment after ICI. We calculated the percentage increase in tumor volume before (TGR1) and after immunotherapy (TGR2). Finally, we compared TGR1 and TGR2. If no progressive disease (PD), the group was disease control (DC). If PD but TGR2 < TGR1, it was called LvPD and if TGR2 ⩾ TGR1, HvPD. Results: A total of 61 patients who received ICIs and 33 treated with chemotherapy (ChT) were included. In ICI group, 18 patients were HvPD, 22 LvPD, 21 DC. Median OS was 4.4 months (95% CI: 2.0–6.8, reference) for HvPD, 7.1 months (95% CI 5.4–8.8) for LvPD, p = 0.018, and 20.9 months (95% CI: 12.5–29.3) for DC, p < 0.001. In ChT group, 7 were categorized as HvPD, 17 as LvPD and 9 as DC. No difference in OS was observed in the ChT group (p = 0.786) Conclusion: In the presence of PD, a decrease in TGR may result in a clinical benefit in patients treated with ICI but not with chemotherapy. Monitoring TGR changes after ICIs administration can help physician in deciding to treat beyond PD.

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a mobile vehicle and the arcs are associated to pre-assigned geometric paths that connect these positions. BASP consists in finding the minimum-time path between two nodes. Differently from SP, we require that the vehicle satisfy bounds on maximum and minimum acceleration and speed, that depend on the vehicle position on the currently traveled arc. We prove that BASP is NP-hard and define solution algorithm that achieves polynomial time-complexity under some additional hypotheses on problem data.