TY - GEN

T1 - Incremental single source shortest paths in sparse digraphs

AU - Chechik, Shiri

AU - Zhang, Tianyi

N1 - Publisher Copyright:
© 2021 by SIAM

PY - 2021

Y1 - 2021

N2 - Given a directed graph G = (V, E, ω) with positive integer edge weights that undergoes a sequence of edge insertions, we are interested in maintaining approximate single-source shortest paths in the incremental graph G. In a very recent paper, [Gutenberg et al., 2020] proposed a deterministic algorithm for this problem with Õ(n2 log W) total update time, where n = |V | and W denotes the maximum edge weight. When the underlying graph is super dense, namely, the total number of insertions m is Ω(- n2), their upper bound is essentially optimal. For sparse graphs, the only known result is due to [Henzinger et al., 2014], whose algorithm is randomized and works in Õ(mn0.9 log W) total update time under the assumption of oblivious non-adaptive adversary. In this work, we provide two algorithms for this problem when the graph is sparse. The first one is a simple deterministic algorithm with Õ(m5/3 log W) total update time. The second one is a randomized algorithm with Õ((mn1/2 + m7/5) log W) total update time, which improves over both previous results when m = O(n1.42); moreover, this randomized algorithm plays against adaptive adversaries. Our algorithms are the first to break the O(mn) bound with adaptive adversaries for sparse graphs.

AB - Given a directed graph G = (V, E, ω) with positive integer edge weights that undergoes a sequence of edge insertions, we are interested in maintaining approximate single-source shortest paths in the incremental graph G. In a very recent paper, [Gutenberg et al., 2020] proposed a deterministic algorithm for this problem with Õ(n2 log W) total update time, where n = |V | and W denotes the maximum edge weight. When the underlying graph is super dense, namely, the total number of insertions m is Ω(- n2), their upper bound is essentially optimal. For sparse graphs, the only known result is due to [Henzinger et al., 2014], whose algorithm is randomized and works in Õ(mn0.9 log W) total update time under the assumption of oblivious non-adaptive adversary. In this work, we provide two algorithms for this problem when the graph is sparse. The first one is a simple deterministic algorithm with Õ(m5/3 log W) total update time. The second one is a randomized algorithm with Õ((mn1/2 + m7/5) log W) total update time, which improves over both previous results when m = O(n1.42); moreover, this randomized algorithm plays against adaptive adversaries. Our algorithms are the first to break the O(mn) bound with adaptive adversaries for sparse graphs.

UR - http://www.scopus.com/inward/record.url?scp=85105286459&partnerID=8YFLogxK

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AN - SCOPUS:85105286459

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

SP - 2463

EP - 2477

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2021

A2 - Marx, Daniel

PB - Association for Computing Machinery

Y2 - 10 January 2021 through 13 January 2021

ER -