Finding communities in evolving networks is a difficult task and raises issues different from the classic static detection case. We introduce an approach based on the recent vertex-centred paradigm. The proposed algorithm, named DynLOCNeSs, detects communities by scanning and evaluating each vertex neighbourhood, which can be done independently in a parallel way. It is done by means of a preference measure, using these preferences to handle community changes. We also introduce a new vertex neighbourhood preference measure, CWCN, more efficient than current existing ones in the considered context. Experimental results show the relevance of this measure and the ability of the proposed approach to detect classical community evolution patterns such as grow-shrink and merge-split.
The major drawback with these algorithms is that they loose one of the initial benefits of the leader-based approach, i.e. lightness and flexibility. Built on top of Top-Leaders, Evo-Leaders @cite_5 adds a costly split-merge of community at each time step. mux-LICOD @cite_10 uses degree centrality and shortest path calculation to compare leaders and followers. Shortest path computation can be costly if used for each vertex to each potential leader. It also relies on an aggregation phase repeated until stabilisation, though experiments do not reveal whether the stabilisation is fast or not. Finally, 's method @cite_24 relies on a fitness function and a set of ad-hoc update rules and pruning over updates. It is hard to know however how efficient this policy is, as the experiments proposed by the authors are limited to a comparison with re-computation of the static counterpart. While faster than static re-computation (which is generally expected for specifically dynamic-addressed algorithms), the proposed @math -score comparison with the set of static re-computed instances is not meaningful, as static re-computation has been proved to give unstable results @cite_11 .
@cite_24 @cite_5 @cite_10 @cite_11
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The election of an eventual leader in an asynchronous system prone to process crashes is an important problem of fault-tolerant distributed computing. This problem is known as the implementation of the failure detector Ω. Nearly all papers that propose algorithms implementing such an eventual leader service consider a static system. In contrast this paper considers a dynamic system, i.e. a system in which processes can join and leave. The paper has three main contributions. It first proposes a specification of Ω suited to dynamic systems. Then, it presents and proves correct two algorithms implementing this specification. Finally, the paper discusses the notion of an eventual leader suited to dynamic systems. It introduces an additional property related to system stability. The design of an algorithm satisfying this last property remains an open challenging problem. We present two algorithms for dynamically maintaining a spanning forest of a graph undergoing edge insertions and deletions. Our algorithms guarantee worst-case update time and work against an adaptive adversary, meaning that an edge update can depend on previous outputs of the algorithms. We provide the first polynomial improvement over the long-standing O(√n) bound of [Frederickson STOC'84, Eppstein, Galil, Italiano and Nissenzweig FOCS'92] for such type of algorithms. The previously best improvement was O(√n (loglogn)2 logn) [Kejlberg-Rasmussen, Kopelowitz, Pettie and Thorup ESA'16]. We note however that these bounds were obtained by deterministic algorithms while our algorithms are randomized. Our first algorithm is Monte Carlo and guarantees an O(n0.4+o(1)) worst-case update time, where the o(1) term hides the O(√loglogn logn) factor. Our second algorithm is Las Vegas and guarantee an O(n0.49306) worst-case update time with high probability. Algorithms with better update time either needed to assume that the adversary is oblivious (e.g. [Kapron, King and Mountjoy SODA'13]) or can only guarantee an amortized update time. Our second result answers an open problem by To the best of our knowledge, our algorithms are among a few non-trivial randomized dynamic algorithms that work against adaptive adversaries. The key to our results is a decomposition of graphs into subgraphs that either have high expansion or sparse. This decomposition serves as an interface between recent developments on (static) flow computation and many old ideas in dynamic graph algorithms: On the one hand, we can combine previous dynamic graph techniques to get faster dynamic spanning forest algorithms if such decomposition is given. On the other hand, we can adapt flow-related techniques (e.g. those from [Khandekar, Rao and Vazirani STOC'06], [Peng SODA'16], and [Orecchia and Zhu SODA'14]) to maintain such decomposition. To the best of our knowledge, this is the first time these flow techniques are used in fully dynamic graph algorithms. We consider the problem of electing a leader among nodes in a highly dynamic network where the adversary has unbounded capacity to insert and remove nodes (including the leader) from the network and change connectivity at will. We present a randomized algorithm that (re)elects a leader in O(Dlog n) rounds with high probability, where D is a bound on the dynamic diameter of the network and n is the maximum number of nodes in the network at any point in time. We assume a model of broadcast-based communication where a node can send only 1 message of O(log n) bits per round and is not aware of the receivers in advance. Thus, our results also apply to mobile wireless adhoc networks, improving over the optimal (for deterministic algorithms) O(Dn) solution presented at FOMC 2011. We show that our algorithm is optimal by proving that any randomized Las Vegas algorithm takes at least Ω(Dlog n) rounds to elect a leader with high probability, which shows that our algorithm yields the best possible (up to constants) ter mination time. Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on randomly sampled paths has been shown to be significantly faster in practice. However, for dynamic networks, no approximation algorithm for betweenness centrality is known that improves on static recomputation. We address this deficit by proposing two incremental approximation algorithms (for weighted and unweighted connected graphs) which provide a provable guarantee on the absolute approximation error. Processing batches of edge insertions, our algorithms yield significant speedups up to a factor of 104 compared to restarting the approximation. This is enabled by investing memory to store and efficiently update shortest paths. As a building block, we also propose an asymptotically faster algorithm for updating the SSSP problem in unweighted graphs. Our experimental study shows that our algorithms are the first to make in-memory computation of a betweenness ranking practical for million-edge semi-dynamic networks. Moreover, our results show that the accuracy is even better than the theoretical guarantees in terms of absolute errors and the rank of nodes is well preserved, in particular for those with high betweenness.