This paper studies approximation algorithms for minimizing power losses in electrical distribution networks, proving hardness results and providing approximations for various configurations.

The paper introduces a non-intrusive variant of index-aware learning for solving differential-algebraic equations (DAEs), ensuring that learned solutions maintain physical consistency like Kirchhoff's…

This paper presents approximation algorithms for the one-way directed Reachability-Preserving Minimum Edge Cut problem in directed graphs.

This paper presents a randomized algorithm that runs in $ ilde{O}(n^2)$ time and, with high probability, guarantees a 2-approximation for all pairs at distance at least $c$ in an undirected, unweighte…

This paper presents an optimized algorithm for computing cut sets of a path set in graph theory and introduces a vectorized computational framework for property calculations.

The paper presents an algorithm for updating a Directed Minimum Spanning Tree using the weighted matroid intersection algorithm and a dynamic auxiliary graph.

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper proves that the maximum of up to 10 real numbers can be exactly represented by a ReLU network with two hidden layers, and shows that the same depth bound holds for all continuous piecewise-…

This paper disproves a conjecture about the longest-path lengths of MaxSTN and MinSTN algorithms for producing $st$-orientations of biconnected graphs.

This book provides a compact, derivation-oriented mathematical primer that connects major families of generative AI models, showing their underlying structural relationships.

The paper develops a minimal dynamical model showing that adaptive softmax routing in Mixture-of-Experts (MoE) layers can undergo abrupt transitions to load imbalance via bifurcation mechanisms.

This paper proves several properties about Extended Frege proof systems and circuit equivalence.

This paper proves that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time.