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Dynamic Graph Triangle Counting

3 posts · Feb 2016 – Jul 2017

What this trail covers

Two Sigma is developing capabilities for analyzing dynamic graphs, specifically focusing on efficiently counting triangles (local and global) in streams of edge insertions and deletions. This involves creating one-pass streaming algorithms that use reservoir sampling to maintain a fixed memory footprint while providing unbiased, low-variance approximations. The goal is to outperform existing methods in accuracy and update time on very large graphs. This post introduces TRIÈST, a suite of sampling algorithms for dynamic graph triangle counting, and Wiggins, an algorithm for detecting valuable information in dynamic networks with limited resources by optimizing a probing schedule through convex optimization and a scalable MapReduce variant.

All Two Sigma trails
  1. TRIEST: Counting Local and Global Triangles in Fully-Dynamic Streams with Fixed Memory SizeThis post introduces TRIÈST, a suite of one-pass streaming algorithms for computing unbiased, low-variance approximations of global and local triangle counts in fully-dynamic graphs. TRIÈST utilizes reservoir sampling and its variants to operate within a user-specified memory size, offering novel concentration bounds and outperforming state-of-the-art approaches in accuracy and update time on large graphs.
  2. TRIÈST: Counting Triangles in Edge StreamsIntroduced TRIÈST, a suite of sampling-based, one-pass algorithms for approximate triangle counting in fully-dynamic edge streams. TRIÈST stores a small, fixed-size subset of edges as a sample to continuously update triangle estimates. It achieves high accuracy and speed, processing up to 100,000 edges per second with an estimation error within 20% of the true value, a significant improvement over previous state-of-the-art.
  3. Wiggins: Detecting Valuable Information in Dynamic Networks with Limited ResourcesThis post introduces Wiggins, an algorithm for detecting valuable information in dynamic networks with limited resources. It addresses the problem of optimizing a probing schedule to minimize the average novelty of undetected items when only a small subset of nodes can be probed at each time step. The algorithm uses convex optimization to compute the optimal schedule and includes a scalable variant for the MapReduce framework. The work also touches upon dynamic graph analysis by presenting a method for triangle counting in dynamic graphs.