Algorithms for Secretary Problems on Graphs and Hypergraphs

We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following secretary problem: Initially given R, and the size of L, the algorithm receives the vertices of L sequentially, in a random order. When a vertex l \in L is seen, all edges incident to l are revealed, together with their weights. The algorithm must immediately either match l to an available vertex of R, or decide that l will remain unmatched. Dimitrov and Plaxton show a 16-competitive algorithm for the transversal matroid secretary problem, which is the special case with weights on vertices, not edges. (Equivalently, one may assume that for each l \in L, the weights on all edges incident to l are identical.) We use a similar algorithm, but simplify and improve the analysis to obtain a better competitive ratio for the more general problem. Perhaps of more interest is the fact that our analysis is easily extended to obtain competitive algorithms for similar problems, such as to find disjoint sets of edges in hypergraphs where edges arrive online. We also introduce secretary problems with adversarially chosen groups. Finally, we give a 2e-competitive algorithm for the secretary problem on graphic matroids, where, with edges appearing online, the goal is to find a maximum-weight acyclic subgraph of a given graph.Comment: 15 pages, 2 figure

A Comparative Analysis of Phytovolume Estimation Methods Based on UAV-Photogrammetry and Multispectral Imagery in a Mediterranean Forest

Management and control operations are crucial for preventing forest fires, especially in Mediterranean forest areas with dry climatic periods. One of them is prescribed fires, in which the biomass fuel present in the controlled plot area must be accurately estimated. The most used methods for estimating biomass are time-consuming and demand too much manpower. Unmanned aerial vehicles (UAVs) carrying multispectral sensors can be used to carry out accurate indirect measurements of terrain and vegetation morphology and their radiometric characteristics. Based on the UAV-photogrammetric project products, four estimators of phytovolume were compared in a Mediterranean forest area, all obtained using the difference between a digital surface model (DSM) and a digital terrain model (DTM). The DSM was derived from a UAV-photogrammetric project based on the structure from a motion algorithm. Four different methods for obtaining a DTM were used based on an unclassified dense point cloud produced through a UAV-photogrammetric project (FFU), an unsupervised classified dense point cloud (FFC), a multispectral vegetation index (FMI), and a cloth simulation filter (FCS). Qualitative and quantitative comparisons determined the ability of the phytovolume estimators for vegetation detection and occupied volume. The results show that there are no significant differences in surface vegetation detection between all the pairwise possible comparisons of the four estimators at a 95% confidence level, but FMI presented the best kappa value (0.678) in an error matrix analysis with reference data obtained from photointerpretation and supervised classification. Concerning the accuracy of phytovolume estimation, only FFU and FFC presented differences higher than two standard deviations in a pairwise comparison, and FMI presented the best RMSE (12.3 m) when the estimators were compared to 768 observed data points grouped in four 500 m2 sample plots. The FMI was the best phytovolume estimator of the four compared for low vegetation height in a Mediterranean forest. The use of FMI based on UAV data provides accurate phytovolume estimations that can be applied on several environment management activities, including wildfire prevention. Multitemporal phytovolume estimations based on FMI could help to model the forest resources evolution in a very realistic way

Hierarchical Up/Down Routing Architecture for Ethernet backbones and campus networks

We describe a new layer two distributed and scalable routing architecture. It uses an automatic hierarchical node identifier assignment mechanism associated to the rapid spanning tree protocol. Enhanced up/down mechanisms are used to prohibit some turns at nodes to break cycles, instead of blocking links like the spannning tree protocol does. The protocol performance is similar or better than other turn prohibition algorithms recently proposed with lower complexity O(Nd) and better scalability. Simulations show that the fraction of prohibited turns over random networks is less than 0.2. The effect of root bridge election on the performance of the protocol is limited both in the random and regular networks studied. The use of hierarchical, tree-descriptive addresses simplifies the routing, and avoids the need of all nodes having a global knowleddge of the network topology. Routing frames through the hierarchical tree at very high speed is possible by progressive decoding of frame destination address, without routing tables or port address learning. Coexistence with standard bridges is achieved using combined devices: bridges that forward the frames having global destination MAC addresses as standard bridges and frames with local MAC frames with the proposed protocol.Publicad