Dynamic algorithms operate on inputs undergoing updates, eg, insertions or deletions of
edges or vertices. After processing each update, the algorithm has to answer queries …

Algebraic techniques have had an important impact on graph algorithms so far. Porting
them, eg, the matrix inverse, into the dynamic regime improved best-known bounds for …

Designing approximate all-pairs distance oracles in the fully dynamic setting is one of the
central problems in dynamic graph algorithms. Despite extensive research on this topic, the …

We present the first non-trivial fully dynamic algorithm maintaining exact single-source
distances in unweighted graphs. This resolves an open problem stated by Sankowski …

We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs,
we show a deterministic fully dynamic data structure with $\tilde {O}(mn^{4/5}) $ worst-case …

Algebraic data structures are the main subroutine for maintaining distances in fully dynamic
graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot …

The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in
theoretical computer science. It asks to compute the distance matrix of a given n-vertex …

This paper presents quantum interior-point methods (QIPMs) tailored to tackle the DC
optimal power flow (OPF) problem using noisy intermediate-scale quantum devices. The …

Abstract Single Source Shortest Paths (SSSP) is among the most well-studied problems in
computer science. In the incremental (resp. decremental) setting, the goal is to maintain …

We present a new distance oracle in the fully dynamic setting: given a weighted undirected
graph $ G=(V, E) $ with $ n $ vertices undergoing both edge insertions and deletions, and …