Shortest path queries in rectilinear worlds

Abstract In this paper, a data structure is given for two and higher dimensional shortest path queries. For a set of n axis-parallel rectangles in the plane, or boxes in d-space, and a fixed target, it is possible with this structure to find a shortest rectilinear path avoiding all rectangles or boxes from any point to this target. Alternatively, it is possible to find the length of the path. The metric considered is a generalization of the Ll-metric and the link metric, where the length of a path is its L1-Iength plus some (fixed) constant times the number of turns on the path. The data structure has size 0« n log n )d-l), and a query takes O(logd-l n) time (plus the output size if the path must be reported). As a byproduct, a relatively simple solution to the single shot problem is obtained; the shortest path between two given points can be computed in time O(ndlogn) for d ~ 3, and in time 0(n 2 ) in the plane

In Reply

We appreciate the interest of Lagier et al. in our article.1 The authors highlighted in their letter the work of Montaigne et al.,2 who have recently published on the circadian rhythm in relation to ischemia reperfusion injury in a single-center retrospective propensity-matched cohort study addressing this subject on 596 (matched-pairs) patients undergoing aor-tic valve replacement with or without coronary artery bypass grafting, together with a single-center randomized study in 88 patients undergoing isolated aortic valve replacement, in which the perioperative myocardial injury has been assessed with the geometric mean of perioperative cardiac troponin T release

Effect of xenon anesthesia compared to sevoflurane and total intravenous anesthesia for coronary artery bypass graft surgery on postoperative cardiac troponin release. an international, multicenter, phase 3, single-blinded, randomized noninferiority trial

Abstract BACKGROUND: Ischemic myocardial damage accompanying coronary artery bypass graft surgery remains a clinical challenge. We investigated whether xenon anesthesia could limit myocardial damage in coronary artery bypass graft surgery patients, as has been reported for animal ischemia models. METHODS: In 17 university hospitals in France, Germany, Italy, and The Netherlands, low-risk elective, on-pump coronary artery bypass graft surgery patients were randomized to receive xenon, sevoflurane, or propofol-based total intravenous anesthesia for anesthesia maintenance. The primary outcome was the cardiac troponin I concentration in the blood 24 h postsurgery. The noninferiority margin for the mean difference in cardiac troponin I release between the xenon and sevoflurane groups was less than 0.15 ng/ml. Secondary outcomes were the safety and feasibility of xenon anesthesia. RESULTS: The first patient included at each center received xenon anesthesia for practical reasons. For all other patients, anesthesia maintenance was randomized (intention-to-treat: n = 492; per-protocol/without major protocol deviation: n = 446). Median 24-h postoperative cardiac troponin I concentrations (ng/ml [interquartile range]) were 1.14 [0.76 to 2.10] with xenon, 1.30 [0.78 to 2.67] with sevoflurane, and 1.48 [0.94 to 2.78] with total intravenous anesthesia [per-protocol]). The mean difference in cardiac troponin I release between xenon and sevoflurane was -0.09 ng/ml (95% CI, -0.30 to 0.11; per-protocol: P = 0.02). Postoperative cardiac troponin I release was significantly less with xenon than with total intravenous anesthesia (intention-to-treat: P = 0.05; per-protocol: P = 0.02). Perioperative variables and postoperative outcomes were comparable across all groups, with no safety concerns. CONCLUSIONS: In postoperative cardiac troponin I release, xenon was noninferior to sevoflurane in low-risk, on-pump coronary artery bypass graft surgery patients. Only with xenon was cardiac troponin I release less than with total intravenous anesthesia. Xenon anesthesia appeared safe and feasible