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We are delighted to announce that a result coauthored by and (from our Theory and Foundations Research Division), along with (University of Waterloo), (Northeastern University), (Tel Aviv University) and (ETH Zurich), has received a best paper award at the upcoming (STOC), 2025. STOC is a flagship international conference in theoretical computer science.

The paper, titled "," tackles a fundamental, textbook edge-coloring problem: Given a graph G with n vertices and m edges, the goal is to assign a color to each edge such that no two edges sharing a common endpoint receive the same color. A classical result by Vizing, dating back to 1960s, proves that any simple graph can always be edge-colored with at most Δ + 1 colors, where Δ is the maximum degree of a vertex. Vizing's original proof is inherently algorithmic and immediately gives an O(mn) time algorithm for computing such a coloring.

This problem has seen a long and influential line of research aimed at designing faster algorithms for this basic task. For over four decades, the best-known runtime was Õ(m√n), a significant barrier that was only broken in 2024 through concurrent, independent works. The recent paper culminates this effort by providing a randomized algorithm that computes a Δ + 1 edge coloring in O(m log Δ) time, a running time that is near-linear in the input size.