# Fully dynamic all-pairs shortest paths with worst-case update-time revisited

@article{Abraham2017FullyDA, title={Fully dynamic all-pairs shortest paths with worst-case update-time revisited}, author={Ittai Abraham and Shiri Chechik and Sebastian Krinninger}, journal={ArXiv}, year={2017}, volume={abs/1607.05132} }

We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case guarantees on the time needed to process a single update (in contrast to related results, the update time is not amortized over a sequence of updates). Our main result is a simple randomized algorithm that for any parameter c > 1 has a worst-case update time of O…

## 46 Citations

### Dynamic Approximate Shortest Paths and Beyond: Subquadratic and Worst-Case Update Time

- Computer Science2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

This paper develops an efficient (1 + ε) -approximation algorithm for this query using fast matrix multiplication and obtains the first dynamic APSP algorithm with subquadratic update time and sublinear query time.

### Single-Source Shortest Paths and Strong Connectivity in Dynamic Planar Graphs

- Computer ScienceESA
- 2020

To the best of the knowledge, this is the first fully dynamic strong-connectivity algorithm achieving both sublinear update time and polylogarithmic query time for an important class of digraphs.

### Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs

- Computer Science, MathematicsESA
- 2019

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that…

### Fully-Dynamic All-Pairs Shortest Paths: Improved Worst-Case Time and Space Bounds

- Computer ScienceSODA
- 2020

These are the first exact dynamic algorithms with truly-subcubic update time \emph{and} space usage and match the worst-case update time of the best previous algorithms and the second algorithm improves upon a Monte-Carlo algorithm in a weaker adversary model with the same running time.

### Fully Dynamic Connectivity Oracles under General Vertex Updates

- Computer Science, MathematicsISAAC
- 2017

Two algorithms are proposed for the following dynamic graph problem: an amortized update time deterministic one and a worst case update time Monte Carlo one that allows an arbitrary number of new vertices to insert.

### Fully Dynamic Algorithms for Minimum Weight Cycle and Related Problems

- Computer Science, MathematicsICALP
- 2021

This work generalizes the exact fully dynamic APSP data structure of Abraham et al. to solve the multiple-pairs shortest paths problem, where one is interested in computing distances for some k fixed source-target pairs after each update, and shows that in such a scenario, Õ((m+ k)n) worst-case update time is possible.

### A Deamortization Approach for Dynamic Spanner and Dynamic Maximal Matching

- Computer Science, MathematicsSODA
- 2019

The first polylogarithmic high-probabilityworst-case time bounds for the dynamic spanner and the dynamic maximal matching problem are presented and a black-box reduction is presented that converts any data structure with worst-case expected update time into one with a high- Probability worst- case update time.

### Dynamic Minimum Spanning Forest with Subpolynomial Worst-Case Update Time

- Computer Science2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

A Las Vegas algorithm for dynamically maintaining a minimum spanning forest of an n-node graph undergoing edge insertions and deletions and guarantees an O(n^{o(1)})} worst-case update time with high probability is presented.

### Near-Optimal Algorithms for Reachability, Strongly-Connected Components and Shortest Paths in Partially Dynamic Digraphs

- Mathematics, Computer ScienceArXiv
- 2020

This thesis presents new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions, and obtains the first randomized data structure to maintain SSR and SCCs in near-optimal total update time in a graph undergoing edge deletions.

### Efficient fully dynamic elimination forests with applications to detecting long paths and cycles

- Computer Science, MathematicsSODA
- 2021

We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data…

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