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

  title={Fully dynamic all-pairs shortest paths with worst-case update-time revisited},
  author={Ittai Abraham and Shiri Chechik and Sebastian Krinninger},
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… 

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

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

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

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

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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

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A Deamortization Approach for Dynamic Spanner and Dynamic Maximal Matching

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

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

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

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Dynamic approximate all-pairs shortest paths in undirected graphs

  • Liam RodittyU. Zwick
  • Computer Science
    45th Annual IEEE Symposium on Foundations of Computer Science
  • 2004
Three dynamic algorithms for the approximate all-pairs shortest paths problem in unweighted undirected graphs, including a fully dynamic algorithm with an expected amortized update time of O(mn/t) and worst-case query time ofO(t).

Fully dynamic all pairs shortest paths with real edge weights

  • C. DemetrescuG. Italiano
  • Computer Science, Mathematics
    Proceedings 2001 IEEE International Conference on Cluster Computing
  • 2001
This work presents the first fully dynamic algorithm for maintaining all pairs shortest paths in directed graphs with real-valued edge weights, and gives a randomized algorithm with one-sided error which supports updates faster in O(S/spl middot/nlog/sup 3/n) amortized time.

Worst-case update times for fully-dynamic all-pairs shortest paths

The first solution to the fully-dynamic all pairs shortest path problem where every update is faster than a recomputation from scratch in Ω(n) time is presented, for a directed graph with arbitrary non-negative edge weights.

Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization

An algorithm with a total update time of Ȏ(n5/2) and constant query time that has an additive error of two in addition to the 1 + ϵ multiplicative error is presented, giving the first improved deterministic algorithm since 1981.

A new approach to dynamic all pairs shortest paths

A fully dynamic algorithm for general directed graphs with non-negative real-valued edge weights that supports any sequence of operations in amortized time per update and unit worst-case time per distance query, where n is the number of vertices.

Deterministic decremental single source shortest paths: beyond the o(mn) bound

This paper presents the first deterministic decremental SSSP algorithm that breaks the Even-Shiloach bound of O(mn) total update time, for unweighted and undirected graphs, and is faster than all existing randomized algorithms.

Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs

A randomized algorithm is obtained which achieves an Õ (mn0.984) expected total update time for SSR and (1 + ε)-approximate SSSP, where Õ(·) hides poly log n and this algorithm serves as a building block for several other dynamic algorithms.

Maintaining all-pairs approximate shortest paths under deletion of edges

A hierarchical scheme for efficiently maintaining all-pairs approximate shortest paths in undirected unweighted graphs under deletions of edges and the first update time algorithm based on this scheme is presented.

A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs

The approximation algorithm is based upon a novel technique for approximately representing all-pairs shortest paths among a selected subset of the nodes by a sparse substitute graph, and is guaranteed to be accurate to within a 1+ $\epsilon$ factor.