TY - GEN

T1 - Fully dynamic all-pairs shortest paths with worst-case update-time revisited

AU - Abraham, Ittai

AU - Chechik, Shiri

AU - Krinninger, Sebastian

N1 - Publisher Copyright:
Copyright © by SIAM.

PY - 2017

Y1 - 2017

N2 - 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 worstcase 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(cn2+2/3 log4/3 n) and answers distance queries correctly with probability 1 - 1/nc, against an adaptive online adversary if the graph contains no negative cycle. The best deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time of O(n2+3/4) and assumes non-negative weights. This is the first improvement for this problem for more than a decade. Conceptually, our algorithm shows that randomization along with a more direct approach can provide better bounds.

AB - 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 worstcase 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(cn2+2/3 log4/3 n) and answers distance queries correctly with probability 1 - 1/nc, against an adaptive online adversary if the graph contains no negative cycle. The best deterministic algorithm is by Thorup [STOC 2005] with a worst-case update time of O(n2+3/4) and assumes non-negative weights. This is the first improvement for this problem for more than a decade. Conceptually, our algorithm shows that randomization along with a more direct approach can provide better bounds.

UR - http://www.scopus.com/inward/record.url?scp=85016204222&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974782.28

DO - 10.1137/1.9781611974782.28

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AN - SCOPUS:85016204222

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 440

EP - 452

BT - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

A2 - Klein, Philip N.

PB - Association for Computing Machinery

T2 - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

Y2 - 16 January 2017 through 19 January 2017

ER -