Covering tree with stars

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.

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The average covering tree value for directed graph games

Journal of Combinatorial Optimization ◽

10.1007/s10878-019-00471-5 ◽

2019 ◽

Vol 39 (2) ◽

pp. 315-333 ◽

Cited By ~ 1

Author(s):

Anna Khmelnitskaya ◽

Özer Selçuk ◽

Dolf Talman

Keyword(s):

Directed Graph ◽

Undirected Graph ◽

Solution Concept ◽

Transferable Utility ◽

Communication Structure ◽

Gravity Center ◽

Dominance Relations ◽

Graph Games ◽

Covering Tree ◽

Transferable Utility Games

Abstract 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.

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Maximal covering tree problems

Naval Research Logistics (NRL) ◽

10.1002/1520-6750(199302)40:1<129::aid-nav3220400109>3.0.co;2-t ◽

1993 ◽

Vol 40 (1) ◽

pp. 129-142 ◽

Cited By ~ 5

Author(s):

Richard Church ◽

John Current

Keyword(s):

Maximal Covering ◽

Covering Tree

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Equivalence of boundary measures on covering trees of finite graphs

Ergodic Theory and Dynamical Systems ◽

10.1017/s014338570000804x ◽

1994 ◽

Vol 14 (3) ◽

pp. 575-597 ◽

Cited By ~ 5

Author(s):

Russell Lyons

Keyword(s):

Harmonic Measure ◽

Open Problem ◽

Finite Graph ◽

Universal Covering ◽

Finite Graphs ◽

Complete Answer ◽

Negatively Curved ◽

Natural Measure ◽

Covering Tree

AbstractLet T be the universal covering tree of a finite graph, G. By analogy with an open problem concerning negatively curved covering manifolds, Kaimanovich asked when two of the three natural measure classes on ∂T can coincide, the three measures being harmonic measure, the Patterson measure, and visibility measure. We provide an almost complete answer and discuss related issues. The answer is quite surprising in some cases.

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Orbit counting in conjugacy classes for free groups acting on trees

Journal of Topology and Analysis ◽

10.1142/s1793525317500261 ◽

2017 ◽

Vol 09 (04) ◽

pp. 631-647 ◽

Cited By ~ 1

Author(s):

George Kenison ◽

Richard Sharp

Keyword(s):

Conjugacy Class ◽

Fundamental Group ◽

Error Term ◽

Free Groups ◽

Universal Covering ◽

Conjugacy Classes ◽

Metric Graph ◽

Groups Acting On Trees ◽

Covering Tree ◽

Extra Assumption

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.

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