Mathematical Foundations of the GraphBLAS · HackerPapers discussions

Mathematical Foundations of the GraphBLAS — mentioned by michelpp

Tue, 05 Mar 2024 23:59:28 GMT

When you consider that a graph and a matrix are isomorphic, doing vector matrix multiplication takes a vector with a set value, say row 4, and multiplies it by a matrix where row 4 has values present that represent edges to the nodes that are adjacent to it (ie "adjacency" matrix). The result is a vector with the next "step" in a BFS across the graph, do that in a loop and you step across the whole graph. A cool result of this is, for example, taking an adjacency matrix and squaring it is the "Friend of a Friend" graph. It takes every node/row and multiplies it by itself, returning a matrix…

Paper and discussion history. A mention is not an endorsement.

Mathematical Foundations of the GraphBLAS — mentioned by espeed

Mon, 08 Apr 2019 23:22:46 GMT

Hi Michel - You're working on a GraphBLAS Postgres implementation [0] -- here's an open question I've been pondering... [0] Postgres GraphBLAS https://github.com/michelp/pggraphblas Now that we have SOTA linear algebra models for graphs [1], logic [2] and the lambda calculus [3] that are being optimized for vectorized parallel compute on modern CPU/GPU/TPUs -- do we have the makings for a unified linear algebra model that obsoletes the relational algebra model in relational DBs? [1] Graph Algorithms in the Language of Linear Algebra (2011)…

Paper and discussion history. A mention is not an endorsement.