The ((k,p))-core model was recently proposed to capture engagement dynamics by considering both intra-community interactions (i.e., the k-core structure) and inter-community interactions (i.e., the p-fraction property...
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The ((k,p))-core model was recently proposed to capture engagement dynamics by considering both intra-community interactions (i.e., the k-core structure) and inter-community interactions (i.e., the p-fraction property). It is a refinement of the classic k-core, by introducing an extra parameter p to customize the engagement within a community at a finer granularity. In this paper, we study the problem of maintaining all (k,p)-cores (essentially, maintaining the p-numbers for all vertices) for dynamic graphs. The existing Global approach conducts a global peeling, almost from scratch, for all vertices whose old p-numbers are within a computed range [p-,p+], and thus is inefficient. We propose a new local approach which conducts local searches starting from the two end-points of the newly inserted or deleted edge, and then iteratively expands the search frontier by including their neighbors. Our algorithm is designed based on several fundamental properties that we prove in this paper to characterize the necessary condition for a vertex's p-number to change. Compared to Global, our local approach implicitly obtains the optimal affected p-number range [p-*,p+*] ⊆ [p-,p+], and further skips many vertices whose p-numbers are within this range. Experimental results show that local is on average two orders of magnitude faster than Global.
Many protocols in ad-hoc networks use dominating and connected dominating sets, for example for broadcasting and routing. For large ad hoc networks the construction of such sets should be local in the sense that each ...
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ISBN:
(纸本)9783540787723
Many protocols in ad-hoc networks use dominating and connected dominating sets, for example for broadcasting and routing. For large ad hoc networks the construction of such sets should be local in the sense that each node of the network should make decisions based only on the information obtained from nodes located a constant number of hops from it. In this paper we use the location awareness of the network, i.e. the knowledge of position of nodes in the plane to provide local, constant approximation, deterministic algorithms for the construction of dominating and connected dominating sets of a Unit Disk Graph (UDG). The size of the constructed set, in the case of the dominating set, is shown to be 5 times the optimal, while for the connected dominating set 7.453 + epsilon the optimal, for any arbitrarily small epsilon > 0. These are to our knowledge the first local algorithms whose time complexities and approximation bounds are independent of the size of the network.
local digital algorithms based on nxa <-xn configuration counts are commonly used within science for estimating intrinsic volumes from binary images. This paper investigates multigrid convergence of such algorithms...
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local digital algorithms based on nxa <-xn configuration counts are commonly used within science for estimating intrinsic volumes from binary images. This paper investigates multigrid convergence of such algorithms. It is shown that local algorithms for intrinsic volumes other than volume are not multigrid convergent on the class of convex polytopes. In fact, counter examples are plenty. On the other hand, for convex particles in 2D with a lower bound on the interior angles, a multigrid convergent local algorithm for the Euler characteristic is constructed. Also on the class of r-regular sets, counter examples to multigrid convergence are constructed for the surface area and the integrated mean curvature.
A way of improving the performance of a distributed algorithm is rendering a coloring strategy into an algorithm known as efficient in the nondistributed case. In this paper it is shown that certain sequential colorin...
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A way of improving the performance of a distributed algorithm is rendering a coloring strategy into an algorithm known as efficient in the nondistributed case. In this paper it is shown that certain sequential coloring algorithm heuristics like largest-first (LF), smallest-last (SL), and saturation largest-first (SLF), as applied to some classes of graphs and to special cases of vertex coloring in distributed algorithms, produce an optimal or near-optimal coloring.
Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing - and yet poorly understood-dichotomy. Either simple local algorithms succeed in estimating the object of interes...
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ISBN:
(纸本)9781450345286
Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing - and yet poorly understood-dichotomy. Either simple local algorithms succeed in estimating the object of interest, or even sophisticated semi-definite programming (SDP) relaxations fail. In order to explore this phenomenon, we study a classical SDP relaxation of the minimum graph bisection problem, when applied to Erdos-Renyi random graphs with bounded average degree d > 1, and obtain several types of results. First, we use a dual witness construction (using the so-called non-backtracking matrix of the graph) to upper bound the SDP value. Second, we prove that a simple local algorithm approximately solves the SDP to within a factor 2d(2)/(2d(2) + d - 1) of the upper bound. In particular, the local algorithm is at most 8/9 suboptimal, and 1 + O(1/d) suboptimal for large degree. We then analyze a more sophisticated local algorithm, which aggregates information according to the harmonic measure on the limiting Galton-Watson (GW) tree. The resulting lower bound is expressed in terms of the conductance of the GW tree and matches surprisingly well the empirically determined SDP values on large-scale Erdos-Renyi graphs. We finally consider the planted partition model. In this case, purely local algorithms are known to fail, but they do succeed if a small amount of side information is available. Our results imply quantitative bounds on the threshold for partial recovery using SDP in this model.
Community detection aims to discover and reveal community structures in complex networks. Some community detection method is called local methods that only apply local information in discovering steps. local community...
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Community detection aims to discover and reveal community structures in complex networks. Some community detection method is called local methods that only apply local information in discovering steps. local community detection methods are actually an attempt to increase efficiency in large-scale networks. Most of local community detection methods concentrate on finding the important nodes as initial communities. The quality of the detected communities fundamentally depends on the selected important nodes as community cores. Most of the existing works have disadvantages such as low accuracy, weak scalable, and instability in outcomes that makes the algorithm to detect different communities in each run. In order to solve these problems, this paper proposes a novel local community detection based on high importance nodes Ranking (LCDR). In the proposed algorithm, a new index for computing node importance is presented. With regards to the network locality, the proposed index can fully reflect the node importance of all nodes in the network. LCDR method initially selects important nodes to expand the initial communities based on a local similarity criterion until all nodes become members of one of the communities. Finally, it merges the discovered communities to form final community structures. Experiments on real and synthetic networks show that LCDR can significantly improve the accuracy of communities. Correspondingly, it is promising in different settings based on accuracy and modularity with near-linear time complexity. (C) 2020 Elsevier B.V. All rights reserved.
The non-destructive on-tree measurement of the chemical quality attributes of fruits belonging to the Citrus genus using rapid spectral sensors is of vital interest to citrus growers, allowing them to carry out a sele...
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The non-destructive on-tree measurement of the chemical quality attributes of fruits belonging to the Citrus genus using rapid spectral sensors is of vital interest to citrus growers, allowing them to carry out a selective harvest of any species of Citrus fruit. With this objective, the viability of using of a handheld portable near infrared spectroscopy (NIRS) instrument to predict soluble solid content (SSC), pH, titratable acidity (TA), maturity index and BrimA, in order to measure the optimum harvest time in a group made up of 608 samples belonging to the Citrus genus (378 oranges and 230 mandarins) was evaluated. For each of the parameters analysed, both non-linear regression (local algorithm) and linear regression (Modified Partial Least Squares, MPLS) strategies were designed and compared. The use of the local algorithm in the sample group of oranges and mandarins for all the parameters analysed allowed to obtain more robust models than those obtained with MPLS regression, and it could also be extended more easily when routinely applied. The results confirm that NIRS technology combined with non-linear regression strategies such as the local algorithm can indeed respond to the needs of the Citrus growers and help them to set the optimum harvest time, in this case of oranges and mandarins, by predicting the chemical quality parameters in situ. (C) 2019 Elsevier B.V. All rights reserved.
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