The average covering tree value for directed graph games

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.

Orbit counting in conjugacy classes for free groups acting on trees

In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for the number of elements in a fixed conjugacy class for which the associated displacement of a given base vertex in the universal covering tree is at most T. Under a mild extra assumption we also obtain a polynomial error term.

Research on Fast Application Layer Tree Multicast Algorithm Based on End-to-End Measurement

Application Layer Multicast (ALM) is more flexible than that in IP layer and easy to optimize for specific applications, so the research on it has become a hotspot. Aiming at the problem of most ALM protocol ignoring bandwidth of covering tree, the paper presented a new heuristic algorithm Max-Delta, which inferred the underlying link topology using end-to-end measurement technology. On the basis of this, a kind of Fast Application layer Tree (FAT) algorithm to construct covering tree was proposed to meet the requirements of bandwidth. In addition, the algorithm's time complexity was also analyzed. Simulation results show that Max-Delta algorithm can obtain network topology accurately with less network measurement times comparing with random measurement algorithm and longest path measurement algorithm.

Contribution to the diversity of soil mites (Acari, Gamasida) in southern Croatia (Dalmatia), with some ecological and zoogeographical notes

Contribution to the diversity of soil mites (Acari, Gamasida) in southern Croatia (Dalmatia), with some ecological and zoogeographical notes The species diversity of soil gamasid mites (Acari) in southern Croatia (Dalmatia) was studied in August 2002. In the Krka National Park, Brač Island, and near the town of Makarska, 320 samples were collected from various microhabitats: soil, grass and moss ground cover, wet moss, needle litter, moss covering tree trunks, and decaying wood). Altogether, 2097 mites of 56 gamasid species were recorded. Dominant species were: Polyaspis patavinus (Brač Island), Zercon fageticola (Makarska), and Cheiroseius serratus (Krka National Park). Analyses of ecological preferences and zoogeographic distribution were made for Polyaspis patavinus, Cheiroseius serratus, Zercon fageticola, Z. berlesei, Z. athiasi, Asca nova and A. aphidioides.

Bipartite Random Graphs and Cuckoo Hashing

International audience The aim of this paper is to extend the analysis of Cuckoo Hashing of Devroye and Morin in 2003. In particular we make several asymptotic results much more precise. We show, that the probability that the construction of a hash table succeeds, is asymptotically $1-c(\varepsilon)/m+O(1/m^2)$ for some explicit $c(\varepsilon)$, where $m$ denotes the size of each of the two tables, $n=m(1- \varepsilon)$ is the number of keys and $\varepsilon \in (0,1)$. The analysis rests on a generating function approach to the so called Cuckoo Graph, a random bipartite graph. We apply a double saddle point method to obtain asymptotic results covering tree sizes, the number of cycles and the probability that no complex component occurs.