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Space-Efficient Fully Dynamic DFS in Undirected Graphs

Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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This paper is an extended version of our paper published in WALCOM2017, Entitled “A Space-Efficient Algorithm for the Dynamic DFS Problem in Undirected Graphs”.
Current address: NTT Communication Science Laboratories, Kyoto 619-0237, Japan.
Algorithms 2019, 12(3), 52; https://doi.org/10.3390/a12030052
Received: 30 November 2018 / Revised: 15 February 2019 / Accepted: 21 February 2019 / Published: 27 February 2019
(This article belongs to the Special Issue Efficient Data Structures)
Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions. View Full-Text
Keywords: dynamic graph; depth-first search; biconnectivity; 2-edge-connectivity dynamic graph; depth-first search; biconnectivity; 2-edge-connectivity
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MDPI and ACS Style

Nakamura, K.; Sadakane, K. Space-Efficient Fully Dynamic DFS in Undirected Graphs . Algorithms 2019, 12, 52. https://doi.org/10.3390/a12030052

AMA Style

Nakamura K, Sadakane K. Space-Efficient Fully Dynamic DFS in Undirected Graphs . Algorithms. 2019; 12(3):52. https://doi.org/10.3390/a12030052

Chicago/Turabian Style

Nakamura, Kengo; Sadakane, Kunihiko. 2019. "Space-Efficient Fully Dynamic DFS in Undirected Graphs " Algorithms 12, no. 3: 52. https://doi.org/10.3390/a12030052

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