Algorithms on evolving graphs

Anagnostopoulos, Aris; Kumar, Ravi; Mahdian, Mohammad; Upfal, Eli; Vandin, Fabio

doi:10.1145/2090236.2090249

Cited by 32 publications

(16 citation statements)

References 9 publications

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“…In the more minimalist edge probing model (see e.g. [1]), a query allows to check for an arc's existence. An algorithm obeying the exploration model is called a local algorithm, and its goal is to evaluate one or more nodes in terms of some global graph metric using as few queries as possible -the number of queries is the cost incurred by the algorithm.…”

Section: Graph Exploration Modelsmentioning

confidence: 99%

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The power of local information in PageRank

Bressan

Peserico

Pretto

2013

Proceedings of the 22nd International Conference on World Wide Web

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How large a fraction of a graph must one explore to rank a small set of nodes according to their PageRank scores? We show that the answer is quite nuanced, and depends crucially on the interplay between the correctness guarantees one requires and the way one can access the graph. On the one hand, assuming the graph can be accessed only via "natural" exploration queries that reveal small pieces of its topology, we prove that deterministic and Las Vegas algorithms must in the worst case perform n − o(n) queries and explore essentially the entire graph, independently of the specific types of query employed. On the other hand we show that, depending on the types of query available, Monte Carlo algorithms can perform asymptotically better: if allowed to both explore the local topology around single nodes and access nodes at random in the graph they need Ω(n 2/3 ) queries in the worst case, otherwise they still need Ω(n) queries similarly to Las Vegas algorithms. All our bounds generalize and tighten those already known, cover the different types of graph exploration queries appearing in the literature, and immediately apply also to the problem of approximating the PageRank score of single nodes.

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Section: Graph Exploration Modelsmentioning

confidence: 99%

“…Theorem 10. Choose an integer k ≥ 2, a damping factor α ∈ (0, 1), a separation ǫ > 0, and a score function Θ(1/x) ≤ p(x) ≤ Θ (1). Under any graph exploration model, for any Monte Carlo local ranking algorithm MC with confidence 1 k!…”

Section: Lower Bounds For All Graph Exploration Modelsmentioning

confidence: 99%

The power of local information in PageRank

Bressan

Peserico

Pretto

2013

Proceedings of the 22nd International Conference on World Wide Web

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“…Zhang and Li [12] consider how to find shortest paths in an evolving graph. Anagnostopoulos et al [2] study (s, t)-connectivity and minimum spanning trees in evolving graphs. Bahmani et al [3] give several PageRank algorithms for evolving graphs and they analyze these algorithms both theoretically and experimentally.…”

Section: Previous Work On Evolving Datamentioning

confidence: 99%

Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data

Vial¹,

Devanny

Eppstein

et al. 2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an adversary randomly swaps the order of adjacent items in the true sorted order. Previous work studies only two versions of quicksort, and has a gap between the lower bound of Ω(n) and the best upper bound of O(n log log n). The experiments we perform in this paper provide empirical evidence that some quadratic-time algorithms such as insertion sort and bubble sort are asymptotically optimal for any constant rate of random swaps. In fact, these algorithms perform as well as or better than algorithms such as quicksort that are more efficient in the traditional algorithm analysis model.

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“…Numerous models taking in account topological changes over time have have been proposed since several decades, to quote only a few, [1,2,3,7,8,9,10]. Some works aim at unifying most of the above approaches.…”

Section: Introductionmentioning

confidence: 99%

The Next 700 Impossibility Results in Time-Varying Graphs

Braud-Santoni

Dubois

Kaaouachi

et al. 2016

IJNC

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We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define correctly the convergence of TVG sequences. Next, we provide a general framework that formally proves the convergence of the sequence of executions of any deterministic algorithm over TVGs of any convergent sequence of TVGs. Finally, we illustrate the relevance of the above result by proving that no deterministic algorithm exists to compute the underlying graph of any connected-over-time TVG, i.e., any TVG of the weakest class of long-lived TVGs. *

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Algorithms on evolving graphs

Cited by 32 publications

References 9 publications

The power of local information in PageRank

The power of local information in PageRank

Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data

The Next 700 Impossibility Results in Time-Varying Graphs

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