22 research outputs found
Optimal allocation of defibrillator drones in mountainous regions
Responding to emergencies in Alpine terrain is quite challenging as air
ambulances and mountain rescue services are often confronted with logistics
challenges and adverse weather conditions that extend the response times
required to provide life-saving support. Among other medical emergencies,
sudden cardiac arrest (SCA) is the most time-sensitive event that requires the
quick provision of medical treatment including cardiopulmonary resuscitation
and electric shocks by automated external defibrillators (AED). An emerging
technology called unmanned aerial vehicles (or drones) is regarded to support
mountain rescuers in overcoming the time criticality of these emergencies by
reducing the time span between SCA and early defibrillation. A drone that is
equipped with a portable AED can fly from a base station to the patient's site
where a bystander receives it and starts treatment. This paper considers such a
response system and proposes an integer linear program to determine the optimal
allocation of drone base stations in a given geographical region. In detail,
the developed model follows the objectives to minimize the number of used
drones and to minimize the average travel times of defibrillator drones
responding to SCA patients. In an example of application, under consideration
of historical helicopter response times, the authors test the developed model
and demonstrate the capability of drones to speed up the delivery of AEDs to
SCA patients. Results indicate that time spans between SCA and early
defibrillation can be reduced by the optimal allocation of drone base stations
in a given geographical region, thus increasing the survival rate of SCA
patients
An SDP approach to multi-level crossing minimization
We present an approach based on semidefinite programs (SDP) to tackle the multi-level crossing minimization prob- lem. Thereby, we are given a layered graph (i.e., the graphÂŽs vertices are assigned to multiple parallel levels) and ask for an ordering of the nodes on their levels such that, when draw- ing the graph with straight lines, the resulting number of crossings is minimized. Solving this step is crucial in the probably most widely used graph drawing scheme, the so- called Sugiyama framework. The problem has received a lot of attention both in the field of heuristics and exact methods. For a long time, integer linear programming (ILP) approaches were the only exact algorithms applicable at least to small graphs. Recently, SDP formulations for the special case of two levels were proposed and dominated the ILP for dense instances. In this paper, we present a new SDP formulation for the general multi-level version that, for two-levels, is even stronger than the aforementioned specialized SDP. As a side- product, we also obtain an SDP-based heuristic which in practice always gives (near-)optimal solutions. We conduct a large set of experiments, both on random- ized and on real-world instances, and compare our approach to a state-of-the-art ILP-based branch-and-cut implementa- tion. The SDP clearly dominates for denser graphs, while the ILP approach is usually faster for sparse instances. However, even for such sparse graphs, the SDP solves more instances to optimality than the ILP. In fact, there is no single instance the ILP solved, which the SDP did not. Overall, our experi- ments reveal that for sparse graphs, one should usually try to find an optimal solution with the ILP first. If this approach does not solve the instance to optimality within reasonable time, the SDP still has a good chance to do so. Being able to solve larger real-world instances than reported before, we are also able to evaluate heuristics for this problem. In this paper we do so for the traditional barycenter-heuristic (showing that it leaves a large gap to the true optimum) and the state-of-the-art upward-planarization method (showing that it is usually close to the optimum)
Algorithms for convex quadratic programming
Philipp HungerlÀnderKlagenfurt, Alpen-Adria-Univ., Dipl.-Arb., 2008KB2008 26(VLID)241275