A scramble on a connected multigraph is a collection of connected subgraphs that generalizes the notion of a bramble. The maximum order of a scramble, called the scramble number of a graph, was recently developed as a...
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The Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k...
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We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant ...
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We prove that for every complete graph Kt, all graphs G with no induced subgraph isomorphic to a subdivision of Kt have a stable subset of size at least |G|/polylog |G|. This is close to best possible, because for t ...
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A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks using OFDMA techniques, the problems of time, frequency, are more complicated from a cellular sy...
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ISBN:
(纸本)9783800742530
A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks using OFDMA techniques, the problems of time, frequency, are more complicated from a cellular system, due to system architecture and distributed control and management. This paper focuses on OFDMA wireless mesh network systems and the problem of time/frequency resource allocation, particularly with regard to subcarriers. Advanced graph theory tools are used for time/frequency resource allocation in an arbitrary architecture using to and for a square grid allocation and allow frequency reuse.
The Jacobian is an algebraic invariant of a graph which is often seen in analogy to the class group of a number field. In particular, there have been multiple investigations into the Iwasawa theory of graphs with the ...
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Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al. PODC 2019;Ghaf...
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Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al. PODC 2019;Ghaffari-Uitto SODA 2019), we investigate the complexity of ruling set problems in this model. The MPC model has become very popular as a model for large-scale distributed computing and it comes with the constraint that the memory-per-machine is strongly sublinear in the input size. For graph problems, extremely fast MPC algorithms have been designed assuming Ω˜(n) memory-per-machine, where n is the number of nodes in the graph (e.g., the O(log log n) MIS algorithm of Ghaffari et al., PODC 2018). However, it has proven much more difficult to design fast MPC algorithms for graph problems in the low-memory MPC model, where the memory-per-machine is restricted to being strongly sublinear in the number of nodes, i.e., O(nΕ) for 0 1/6 ∆) rounds whp, in the low-memory MPC model. We then extend this result to β-ruling sets for any integer β > 1. Specifically, we show that a β-ruling set can be computed in the low-memory MPC model with O(nΕ) memory-per-machine in Õ(β · log1/(2β+1−2) ∆) rounds, whp. From this it immediately follows that a β-ruling set for β = Ω(log log log ∆)-ruling set can be computed in in just O(β log log n) rounds whp. The above results assume a total memory of Õ(m + n1+Ε). We also present algorithms for β-ruling sets in the low-memory MPC model assuming that the total memory over all machines is restricted to Õ(m). These algorithms are all substantially faster than the Ghaffari-Uitto (formula precented)-round MIS algorithm in the low-memory MPC model. All our results follow from a Sample-and-Gather Simulation Theorem that shows how random-sampling-based Congest algorithms can be efficiently simulated in the low-memory MPC model. We expect this simulation theorem to be of independent interest beyond the ruling set algorithms derived here. Copyri
Evaluating the performance of researchers and measuring the impact of papers written by scientists is the main objective of citation analysis. Various indices and metrics have been proposed for this. In this paper, we...
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ISBN:
(纸本)9781467364300
Evaluating the performance of researchers and measuring the impact of papers written by scientists is the main objective of citation analysis. Various indices and metrics have been proposed for this. In this paper, we propose a new citation index CITEX, which gives normalized scores to authors and papers to determine their rankings. To the best of our knowledge, this is the first citation index which simultaneously assigns scores to both authors and papers. Using these scores, we can get an objective measure of the reputation of an author and the impact of a paper. We model this problem as an iterative computation on a publication graph, whose vertices are authors and papers, and whose edges indicate which author has written which paper. We prove that this iterative computation converges in the limit, by using a powerful theorem from linear algebra. We run this algorithm on several examples, and find that the author and paper scores match closely with what is suggested by our intuition. The algorithm is theoretically sound and runs very fast in practice. We compare this index with several existing metrics and find that CITEX gives far more accurate scores compared to the traditional metrics.
We consider a natural, yet seemingly not much studied, extremal problem in bipartite graphs. A bi-hole of size t in a bipartite graph G is a copy of Kt,t in the bipartite complement of G. Let f(n, ∆) be the largest k ...
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Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these D...
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