Simons Institute | Panel: Reactive Synthesis - Open Questions and Challenges @SimonsInstituteTOC | Uploaded 2 months ago | Updated 7 hours ago
(Bernd Finkbeiner, Orna Kupferman, and Moshe Vardi)
Synthesis of Models and Systems

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$Sublinear Insights: A Faster (Classical) Algorithm for Edge Coloring Sepehr Assadi (University of Waterloo and Rutgers University) https://simons.berkeley.edu/talks/sepehr-assadi-university-waterloo-rutgers-university-2024-06-20 Extroverted Sublinear Algorithms Vizings theorem states that every graph with maximum degree Delta admits a proper (Delta+1) edge coloring. The state-of-the-art algorithms for finding such a coloring on n-vertex m-edge graphs take O(msqrt(n)) time and date back to the 80s. In this talk, we present a very recent randomized algorithm for finding a Delta+O(log n) coloring in O(m*log(Delta)) time, namely, a near-linear time algorithm for a near-Vizings theorem. This algorithm is inspired by several tools developed in the study of sublinear algorithms. As a corollary of this result and Vizings original approach, we also obtain an O(n^2 log(n)) expected time algorithm for the (Delta+1) edge coloring problem. This is nearly optimal for dense graphs and improves upon the longstanding O(n^{2.5}) bounds of prior work for Vizings theorem in almost four decades. Based on https://arxiv.org/abs/2405.13371 (see also https://arxiv.org/abs/2405.15449 for an independent and concurrent work that obtains an ~O(m*n^{1/3}) time randomized algorithm for Vizings theorem)$

Panel: Reactive Synthesis - Open Questions and Challenges @SimonsInstituteTOC