Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering

@article{Pashanasangi2021FasterAG,
  title={Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering},
  author={Noujan Pashanasangi and C. Seshadhri},
  journal={Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery \& Data Mining},
  year={2021}
}
  • Noujan Pashanasangi, C. Seshadhri
  • Published 5 June 2021
  • Computer Science, Mathematics
  • Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining
Triangle counting is a fundamental technique in network analysis, that has received much attention in various input models. The vast majority of triangle counting algorithms are targeted to static graphs. Yet, many real-world graphs are directed and temporal, where edges come with timestamps. Temporal triangles yield much more information, since they account for both the graph topology and the timestamps. Temporal triangle counting has seen a few recent results, but there are varying… 

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SHOWING 1-10 OF 59 REFERENCES
Triangle counting in large networks: a review
TLDR
The existing methods of triangle counting, ranging from sequential to parallel, single‐machine to distributed, exact to approximate, and off‐line to streaming are discussed, and experimental results of performance comparison among a set of approximate triangle counting methods are presented.
A sampling framework for counting temporal motifs
TLDR
A sampling framework is developed that sits as a layer on top of existing exact counting algorithms and enables fast and accurate memory-efficient estimates of temporal motif counts, and can achieve one to two orders of magnitude speedups with minimal and controllable loss in accuracy on a number of datasets.
ESCAPE: Efficiently Counting All 5-Vertex Subgraphs
TLDR
It is proved that it suffices to enumerate only four specific subgraphs (three of them have less than 5 vertices) to exactly count all 5-vertex patterns, the first practical algorithm for 5- Vertex pattern counting that runs at this scale and is able to compute counts of graphs with tens of millions of edges in minutes on a commodity machine.
Efficient Sampling Algorithms for Approximate Temporal Motif Counting
TLDR
This paper proposes a generic edge sampling algorithm for estimating the number of instances of any temporal motif and devise an improved EWS algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with 3 vertices and 3 edges.
Path Sampling: A Fast and Provable Method for Estimating 4-Vertex Subgraph Counts
TLDR
A sampling algorithm that provably and accurately approximates the frequencies of all 4-vertex pattern subgraphs is provided, based on a novel technique of 3-path sampling and a special pruning scheme to decrease the variance in estimates.
Revisiting Wedge Sampling for Triangle Counting
TLDR
Experiments over large-scale real-world graphs show that proposed mechanism provides five- to a few hundred-folds sampling space reduction and makes as low as ~ 8 × less error when used with the same sampling ratio.
Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE
TLDR
EvoKE is presented, a scalable algorithm that can determine vertex orbits counts for all 5-vertex pattern subgraphs, and it is proved and empirically validate that EVOKE only has a small constant factor overhead over the best (total) 5- Vertex subgraph counter.
Efficient semi-streaming algorithms for local triangle counting in massive graphs
TLDR
This is the first paper that addresses the problem of local triangle counting with a focus on the efficiency issues arising in massive graphs and proposes two approximation algorithms, which are based on the idea of min-wise independent permutations.
A Chronological Edge-Driven Approach to Temporal Subgraph Isomorphism
TLDR
This work presents a new algorithm for temporal subgraph isomorphism that performs the subgraph matching directly on the chronologically sorted edges, and demonstrates how this can produce more meaningful results than traditional static subgraph searches.
Main-memory triangle computations for very large (sparse (power-law)) graphs
...
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