Recent Advances in Fully Dynamic Graph Algorithms

Hanauer, Kathrin; Henzinger, Monika; Schulz, Christof

doi:10.48550/arxiv.2102.11169

Cited by 5 publications

(8 citation statements)

References 183 publications

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“…Instances. We evaluate our algorithms on graphs collected from various resources [4,16,29,35,36,45], which are also used in related studies [30]. Table 1 summarizes the main properties of the benchmark set.…”

Section: Methodsmentioning

confidence: 99%

“…Dynamic algorithms are a widely researched topic. We refer the reader to the recent survey by Hanauer et al [29] for most material related to theoretical and practical dynamic algorithms. Many of the numerous matching applications require matchings with certain properties, like maximal (no edge can be added to M without violating the matching property) or maximum cardinality matchings.…”

Section: Preliminariesmentioning

confidence: 99%

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Fully-dynamic Weighted Matching Approximation in Practice

Angriman¹,

Meyerhenke²,

Schulz³

et al. 2021

Preprint

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Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is based on random walks/paths combined with dynamic programming. The second algorithm has been introduced by Stubbs and Williams without an implementation. Roughly speaking, their algorithm uses dynamic unweighted matching algorithms as a subroutine (within a multilevel approach); this allows us to use previous work on dynamic unweighted matching algorithms as a black box in order to obtain a fully-dynamic weighted matching algorithm. We empirically study the algorithms on an extensive set of dynamic instances and compare them with optimal weighted matchings. Our experiments show that the random walk algorithm typically fares much better than Stubbs/Williams (regarding the time/quality tradeoff), and its results are often not far from the optimum.

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Section: Methodsmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Fully-dynamic Weighted Matching Approximation in Practice

Angriman¹,

Meyerhenke²,

Schulz³

et al. 2021

Preprint

Self Cite

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“…. , 𝑡 𝑚 observed in the network [13,20]. Note that this is extremely different from estimating the temporal betweenness centrality values in temporal networks.…”

Section: Related Workmentioning

confidence: 99%

ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks

Santoro,

Sarpe

2022

Preprint

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In network analysis, the betweenness centrality of a node informally captures the fraction of shortest paths visiting that node. The computation of the betweenness centrality measure is a fundamental task in the analysis of modern networks, enabling the identification of the most central nodes in such networks. Additionally to being massive, modern networks also contain information about the time at which their events occur. Such networks are often called temporal networks. The temporal information makes the study of the betweenness centrality in temporal networks (i.e., temporal betweenness centrality) much more challenging than in static networks (i.e., networks without temporal information). Moreover, the exact computation of the temporal betweenness centrality is often impractical on even moderately-sized networks, given its extremely high computational cost. A natural approach to reduce such computational cost is to obtain high-quality estimates of the exact values of the temporal betweenness centrality. In this work we present ONBRA, the first sampling-based approximation algorithm for estimating the temporal betweenness centrality values of the nodes in a temporal network, providing rigorous probabilistic guarantees on the quality of its output. ONBRA is able to compute the estimates of the temporal betweenness centrality values under two different optimality criteria for the shortest paths of the temporal network. In addition, ONBRA outputs high-quality estimates with sharp theoretical guarantees leveraging on the empirical Bernstein bound, an advanced concentration inequality. Finally, our experimental evaluation shows that ONBRA significantly reduces the computational resources required by the exact computation of the temporal betweenness centrality on several real world networks, while reporting high-quality estimates with rigorous guarantees. CCS CONCEPTS• Mathematics of computing → Probabilistic algorithms; • Theory of computation → Graph algorithms analysis.

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“…We briefly review the most relevant algorithmic results for the dynamic matching problem. For a more detailed survey of the rich literature on dynamic matching and dynamic algorithms more broadly, we refer to the recent survey of Hanauer et al [19].…”

Section: Related Workmentioning

confidence: 99%

“…Let M H , M SH , A(M H ) and A(M SH ) be as in Theorem 3. 19. Let n i the number of frequent augmenting paths of type i ∈ [4]…”

Section: Two Bipartite Matchings Sufficementioning

confidence: 99%

Beating the Folklore Algorithm for Dynamic Matching

Roghani¹,

Saberi²,

Wajc³

2021

Preprint

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The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore algorithm, which maintains a maximal (and hence 2-approximate) matching in O(n) worst-case update time in n-node graphs.We present the first deterministic algorithm which outperforms the folklore algorithm in terms of both approximation ratio and worst-case update time. Specifically, we give a (2−Ω( 1))-approximate algorithm with O( √ n 8 √ m) = O(n 3/4 ) worst-case update time in n-node, m-edge graphs. For sufficiently small constant ǫ > 0, no deterministic (2 + ǫ)-approximate algorithm with worst-case update time O(n 0.99 ) was known. Our second result is the first deterministic (2 + ǫ)-approximate (weighted) matching algorithm with O ǫ (1) • O( 4 √ m) = O ǫ (1) • O( √ n) worst-case update time.

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Recent Advances in Fully Dynamic Graph Algorithms

Cited by 5 publications

References 183 publications

Fully-dynamic Weighted Matching Approximation in Practice

Fully-dynamic Weighted Matching Approximation in Practice

ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks

Beating the Folklore Algorithm for Dynamic Matching

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