We show that the balancing weights technique of Li (2026) actually produces an approximate *pseudo-circulation* of a directed, capacitated graph in $m^{1+o(1)}$ time. Together with standard flow techniques, we obtain an $m^{1+o(1)}$ time maximum flow algorithm that avoids the interior-point method framework of recent almost-linear time algorithms (Chen et al. FOCS 2022, van den Brand et al. FOCS 2024).
The Greedy algorithm of Jain, Mahdian, Markakis, Saberi, and Vazirani was the best Lagrangian-multiplier-preserving (LMP) approximation algorithm for facility location, and thus the engine behind the best $k$-median guarantees, for over two decades. Its $2$-LMP guarantee was only recently broken by a small amount ($(2-...
Rares-Darius Buhai, Vincent Cohen-Addad, Henry L. Fleischmann et al.· 0 citations
K-adaptive Ensembled Partitioning (KEP) is presented, which combines recursive bisection and direct 𝐾 -way search and replaces hard-feasibility Fiduccia–Mattheyses (FM) with an augmented-Lagrangian refinement step (AL-FM) that can cross short infeasible regions before repairing balance.
We investigate bi-objective mixed integer programming to which Benders decomposition can be applied, a widely used technique for exploiting problem structures in real-world applications. Our study focuses on a sustainable supply chain network design problem that aims to minimise both economic and environmental objectiv...
Duleabom An, Chung-Mok Lee, Sophie N. Parragh· 0 citations
Mixed-integer programming (MIP) is a cornerstone in applied optimization, both in industry and academia. Recently, there has been increased attention to finding strong primal solutions quickly. This is reflected, for example, in the development of the NVIDIA cuOpt solver and, most recently, in the new MIPFEAS benchmark...
The Dual-GNN Multilevel Coarsening framework uses learning to guide multilevel graph coarsening while retaining combinatorial search for final decision making and achieves the best mean solution quality among all evaluated methods.
Tian-Feng Chen, Xian-Yue Li· 0 citations
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