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Pinning on Tight Cuts: Improved Algorithm and Bounds for Unsplittable Multicommodity Flows in Outerplanar Graphs

arXiv:2606.04456v1 Announce Type: new Abstract: The multicommodity flow problem in an undirected capacitated graph $G$ is specified by a set of source-sink pairs with nonnegative demands. A flow is feasible if it routes all demands without exceeding the edge capacities, and it is unsplittable if it routes each demand along a single path. Let $\alpha$ be the smallest value such that the existence of a feasible flow implies the existence of an unsplittable flow that exceeds the edge capacities...

arXiv CS 6d ago

Module Lattice Security (Part II): Module Lattice Reduction via Optimal Sign Selection

arXiv:2604.22900v2 Announce Type: replace Abstract: We extend the CDPR's quantum attack from ideal lattices to module lattices over $2^k$-th cyclotomic rings. Using trace orthogonality of the power basis, we decompose a rank-$d$ module into mutually orthogonal rank-$1$ submodules, and apply CDPR's analysis to each independently and return the shortest candidate. The Hermite factor $\exp(\tilde{O}(\sqrt{n}))$ matches the ideal case, with a module reduction factor $\alpha_d=O(1)$ independent...

arXiv CS 7d ago