On the Equivalence among Problems of Bounded Width

In this paper, we introduce a methodology, called decomposition-based reductions, for showing the equivalence among various problems of bounded-width. First, we show that the following are equivalent for any $\alpha > 0$: * SAT can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time, * 3-SAT can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time, * Max 2-SAT can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time, * Independent Set can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time, and * Independent Set can be solved in $O^*(2^{\alpha \mathrm{cw}})$ time, where tw and cw are the tree-width and clique-width of the instance, respectively. Then, we introduce a new parameterized complexity class EPNL, which includes Set Cover and Directed Hamiltonicity, and show that SAT, 3-SAT, Max 2-SAT, and Independent Set parameterized by path-width are EPNL-complete. This implies that if one of these EPNL-complete problems can be solved in $O^*(c^k)$ time, then any problem in EPNL can be solved in $O^*(c^k)$ time.Comment: accepted to ESA 201

Logistic Coordination in Pediatric Liver Transplantation: Criteria for Optimization.

Logistic organization of the transplantation coordination process aims to synchronize the recovery and recipient team and to reduce to a minimum the graft's cold ischemia time (CIT), which, in turn, is known, to have deleterious effects on the graft and recipient, if prolonged. To determine whether variables influencing the different steps in the coordination process might allow for reducing CIT, this study aimed to analyze these variables. Retrospective analysis of 61 pediatric liver transplantations from 2006 to 2015 in the Geneva University Hospitals. Length of donor hepatectomy was increased for split grafts (P < .0001). Length of recipient hepatectomy was longer in the case of previous surgery (P = .06). The recipient team waiting time for the graft was longer for split grafts (P = .01). The graft waiting time at the recipient site was longer for whole grafts (P = .0005) and increased recipient weight (P = .03). The graft waiting time at the donor site was doubled in the case of recovery of organs after the liver by the same team (P = .007). The graft waiting time at the donor and recipient site not surprisingly increased the CIT (P = .007 and < .0001, respectively). CIT depends on waiting times during the entire coordination process, which largely depends on the estimation of hepatectomy lengths. A more accurate estimation, considering graft type and recipient's previous surgery and weight, might allow for decreasing CIT and consequently improve outcomes after pediatric liver transplantation