相关论文: The VPN Tree Routing Conjecture for Outerplanar Ne…
We study the complexity of the Virtual Network Embedding Problem (VNE), which is the combinatorial core of several telecommunication problems related to the implementation of virtualization technologies, such as Network Slicing. VNE is to…
The last in-tree recognition problem asks whether a given spanning tree can be derived by connecting each vertex with its rightmost left neighbor of some search ordering. In this study, we demonstrate that the last-in-tree recognition…
Preferential attachment is the most popular explanation for the emergence of scaling behavior in the World Wide Web, but this explanation has been challenged by the global information hypothesis, the existence of linear preference and the…
A general quantum network for implementing non-local control-unitary gates, between remote parties at minimal entanglement cost, is shown to be a rooted-tree structure. Starting from a five party scenario, we demonstrate the local…
In this paper, we propose a new construction of constantdegree expanders motivated by their application in P2P overlay networks and in particular in the design of robust trees overlay. Our key result can be stated as follows. Consider a…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
We prove a nonuniqueness theorem for Bernoulli site percolation on properly embedded planar graphs, and we obtain a general connectivity principle beyond planarity. Let $G$ be an infinite connected graph properly embedded in $\RR^2$ with…
Future quantum internet relies on large-scale entanglement distribution. Quantum decoherence is a significant obstacle in large-scale networks, which otherwise perform better with multiple paths between the source and destination. We…
Motivated by results of Henry, Pralat and Zhang (PNAS 108.21 (2011): 8605-8610), we propose a general scheme for evolving spatial networks in order to reduce their total edge lengths. We study the properties of the equilbria of two networks…
There are several good reasons you might want to read about uniform spanning trees, one being that spanning trees are useful combinatorial objects. Not only are they fundamental in algebraic graph theory and combinatorial geometry, but they…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
Criticism of Gnutella network scalability has rested on the bandwidth attributes of the original interconnection topology: a Cayley tree. Trees, in general, are known to have lower aggregate bandwidth than higher dimensional topologies…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of…
This work describes probabilistic methods for utilizing random spanning trees generated via a random walk process. Goyal et al. showed that the union of random spanning trees approximates the expansion of every cut of a graph. First, we…
We prove that any quasirandom graph with $n$ vertices and $rn$ edges can be decomposed into $n$ copies of any fixed tree with $r$ edges. The case of decomposing a complete graph establishes a conjecture of Ringel from 1963.
Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the…
Luo, Tian and Wu [Discrete Math. 345 (4) (2022) 112788] conjectured that for any tree $T$ with bipartition $(X,Y)$, every $k$-connected bipartite graph $G$ with minimum degree at least $k+w$, where $w=\max\{|X|,|Y|\}$, contains a tree…
We prove three conjectures regarding the maximization of spectral invariants over certain families of graphs. Our most difficult result is that the join of $P_2$ and $P_{n-2}$ is the unique graph of maximum spectral radius over all planar…
Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example…