Deterministic improved round-trip spanners

Zhu, Chun Jiang; Lam, Kam-Yiu

doi:10.1016/j.ipl.2017.09.008

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…As the future work, we will study whether and how we can achieve similar results for geometric clustering, and how to achieve better computational bounds for the studied problems. We will also study other related problems in the distributed dynamic setting such as low-rank approximation (Bringmann, Kolev, and Woodruff 2017), source-wise and standard round-trip spanner constructions (Zhu and Lam 2017;Zhu and Lam 2018) and cut sparsifier constructions (Abraham et al 2016).…”

Section: Discussionmentioning

confidence: 99%

Communication-Optimal Distributed Dynamic Graph Clustering

Zhu¹,

Zhu²,

Lam

et al. 2019

AAAI

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We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed distributively. We propose communication-efficient algorithms for two well-established communication models namely the message passing and the blackboard models. Given a graph with n nodes that is observed at s remote sites over time [1, t], the two proposed algorithms have communication costsÕ(ns) andÕ(n + s) (Õ hides a polylogarithmic factor), almost matching their lower bounds, Ω(ns) and Ω(n + s), respectively, in the message passing and the blackboard models. More importantly, we prove that at each time point in [1, t] our algorithms generate clustering quality nearly as good as that of centralizing all updates up to that time and then applying a standard centralized clustering algorithm. We conducted extensive experiments on both synthetic and real-life datasets which confirmed the communication efficiency of our approach over baseline algorithms while achieving comparable clustering results.

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Section: Discussionmentioning

confidence: 99%

Communication-Optimal Distributed Dynamic Graph Clustering

Zhu¹,

Zhu²,

Lam

et al. 2019

AAAI

Self Cite

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“…However, for one-way shortest paths, it is even unmeaningful to study spanners because of the well known Ω(n 2 ) size lower bound. In contrast, the stretch-size trade-off for round-trip spanners [24] has been close to the optimal trade-off for spanners in undirected graphs, if we believe Erdős's girth conjecture [10].…”

Section: Introductionmentioning

confidence: 97%

“…In digraphs, round-trip shortest paths have been firstly studied in the context of routing schemes [8,9], and then greatly studied in round-trip graph spanners [20,24,19,23]. In a digraph G, the round-trip shortest path between vertex u and v in G is the concatenation of the one-way shortest path from u to v in G and the one-way shortest path from v to u in G.…”

Section: Introductionmentioning

confidence: 99%

On the VC-dimension of unique round-trip shortest path systems

Zhu

Lam

et al. 2019

Information Processing Letters

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The VC-dimension, which has wide uses in learning theory, has been used in the analysis and design of graph algorithms recently. In this paper, we study the problem of bounding the VCdimension of unique round-trip shortest path set systems (URTSP), which are set systems induced by sets of vertices in unique round-trip shortest paths in directed graphs. We first show that different from the VC-dimensions of set systems induced by unique undirected and directed shortest paths in undirected and directed graphs respectively, the VC-dimension of URTSP can be larger than 3. We then prove that the VC-dimension of URTSP is at most 32. Furthermore, we apply the VC-dimension result to the minimum k-round-trip shortest path cover problem (k-RTSPC), which is to find for a directed graph a minimum vertex set to intersect every round-trip shortest path containing at least k vertices, and derive an upper bound on the size of the vertex set. The k-RTSPC problem can be useful in many real-world applications, including optimal placement of facilities.

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Improved Sourcewise Roundtrip Spanners with Constant Stretch

Stafford,

Zhu

2023

Lecture Notes in Computer Science

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Deterministic improved round-trip spanners

Cited by 5 publications

References 10 publications

Communication-Optimal Distributed Dynamic Graph Clustering

Communication-Optimal Distributed Dynamic Graph Clustering

On the VC-dimension of unique round-trip shortest path systems

Improved Sourcewise Roundtrip Spanners with Constant Stretch

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