A note on the NP-hardness of the separation problem on some valid inequalities for the elementary shortest path problem

International audienc

An efficient cutting plane algorithm for the minimum weighted elementary directed cycle problem in planar digraphs

In this paper, we study the efficiency (both theoretically and computationally) of a class of valid inequalities for the minimum weighted elementary directed cycle problem (MWEDCP) in planar digraphs with negative weight elementary directed cycles. These valid inequalities are called cycle valid inequalities and are parametrized by an integer called inequality’s order. From a theoretical point of view, we prove that separating cycle valid inequalities of order 1 in planar digraph can be done in polynomial time. From a computational point of view, we present a cutting plane algorithm featuring the efficiency of a lifted form of the cycle valid inequalities of order 1. In addition to these lifted valid inequalities, our algorithm is also based on a mixed integer linear formulation of the MWEDCP. The computational results are carried out on randomly generated planar digraph instances of the MWEDCP. For all 29 instances considered, we obtain in average 26.47% gap improvement. Moreover, for some of our instances the strengthening process directly displays the optimal integer elementary directed cycle

Insecticide resistance in Anopheles gambiae sensu lato (Diptera: Culicidae) across different agroecosystems in Niamey, Niger

International audienceMalaria vector control in Niger is currently based on the distribution of insecticide treated nets. However, vectors resistance to insecticides represents a major threat to the current national strategy against malaria. This study aims to characterize the impact of agroecosystems on insecticide resistance in Anopheles gambiae s.l. at Niamey. Larvae collected were reared until emergence. Adults aged 2-5 days were used to assess susceptibility to insecticides (pyrethroids, DDT and bendiocarb) after pre-exposure to piperonyl butoxide (PBO) synergist according to WHO protocols. PCRs were performed to identify the sibling species of An. gambiae complex and characterization resistance mutations (Kdr and ace-1). Overall, An. gambiae s.l. was resistance to pyrethroids and DDT (mortality rates from 1% to 55%) and susceptible to bendiocarb at most sites. Pre-exposure to the PBO synergist resulted in partial restoration of pyrethroid susceptibility. Two species of An. gambiae complex were found: An. arabiensis and An. coluzzii. The presence of An. coluzzii was strongly correlated with agricultural practices (99% in rice cultivation sites). Kdr mutations were found at all sites with kdr-w ranging from 45% to 70% in mosquitoes collected in unirrigated and rice field, respectively, and kdr-e found at 37% to 47% at each type of site, respectively. The ace-1 mutation was detected at low frequency (1%) and only from two rice cultivation sites. The high levels of pyrethroid and DDT resistance detected in Niamey had a strong link with rice cultivation, shown that agriculture is a driver of resistance that can compromise control malaria efforts