
Equivalences between triangle and range query problems
We define a natural class of range query problems, and prove that all pr...
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WRS: Waiting Room Sampling for Accurate Triangle Counting in Real Graph Streams
If we cannot store all edges in a graph stream, which edges should we st...
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Approximate Triangle Counting via Sampling and Fast Matrix Multiplication
There is a trivial O(n^3/T) time algorithm for approximate triangle coun...
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A simple combinatorial algorithm for restricted 2matchings in subcubic graphs – via halfedges
We consider three variants of the problem of finding a maximum weight re...
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Efficient Sampling Algorithms for Approximate Temporal Motif Counting (Extended Version)
A great variety of complex systems ranging from user interactions in com...
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TriPoll: Computing Surveys of Triangles in MassiveScale Temporal Graphs with Metadata
Understanding the higherorder interactions within network data is a key...
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SingleStrip Triangulation of Manifolds with Arbitrary Topology
Triangle strips have been widely used for efficient rendering. It is NP...
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Faster and Generalized Temporal Triangle Counting, via Degeneracy Ordering
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 realworld 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 definitions of temporal triangles. In all cases, temporal triangle patterns enforce constraints on the time interval between edges (in the triangle). We define a general notion (δ_1,3, δ_1,2, δ_2,3)temporal triangles that allows for separate time constraints for all pairs of edges. Our main result is a new algorithm, DOTTT (Degeneracy Oriented Temporal Triangle Totaler), that exactly counts all directed variants of (δ_1,3, δ_1,2, δ_2,3)temporal triangles. Using the classic idea of degeneracy ordering with careful combinatorial arguments, we can prove that DOTTT runs in O(mκlog m) time, where m is the number of (temporal) edges and κ is the graph degeneracy (max core number). Up to log factors, this matches the running time of the best static triangle counters. Moreover, this running time is better than existing. DOTTT has excellent practical behavior and runs twice as fast as existing stateoftheart temporal triangle counters (and is also more general). For example, DOTTT computes all types of temporal queries in Bitcoin temporal network with half a billion edges in less than an hour on a commodity machine.
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