TY - GEN
T1 - Depth-first search using O(n) bits
AU - Asano, Tetsuo
AU - Izumi, Taisuke
AU - Kiyomi, Masashi
AU - Konagaya, Matsuo
AU - Ono, Hirotaka
AU - Otachi, Yota
AU - Schweitzer, Pascal
AU - Tarui, Jun
AU - Uehara, Ryuhei
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2014
Y1 - 2014
N2 - We provide algorithms performing Depth-First Search (DFS) on a directed or undirected graph with n vertices and m edges using only O(n) bits. One algorithm uses O(n) bits and runs in O(mlog n) time. Another algorithm uses n+o(n) bits and runs in polynomial time. Furthermore, we show that DFS on a directed acyclic graph can be done in space [Formula presented], and in polynomial time, and we also give a simple linear-time O(log n)-space algorithm for the depth-first traversal of an undirected tree. Finally, we also show that for a graph having an O(1)-size feedback set, DFS can be done in O(log n) space. Our algorithms are based on the analysis of properties of DFS and applications of the s-t connectivity algorithms due to Reingold and Barnes et al., both of which run in sublinear space.
AB - We provide algorithms performing Depth-First Search (DFS) on a directed or undirected graph with n vertices and m edges using only O(n) bits. One algorithm uses O(n) bits and runs in O(mlog n) time. Another algorithm uses n+o(n) bits and runs in polynomial time. Furthermore, we show that DFS on a directed acyclic graph can be done in space [Formula presented], and in polynomial time, and we also give a simple linear-time O(log n)-space algorithm for the depth-first traversal of an undirected tree. Finally, we also show that for a graph having an O(1)-size feedback set, DFS can be done in O(log n) space. Our algorithms are based on the analysis of properties of DFS and applications of the s-t connectivity algorithms due to Reingold and Barnes et al., both of which run in sublinear space.
UR - http://www.scopus.com/inward/record.url?scp=84945186441&partnerID=8YFLogxK
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U2 - 10.1007/978-3-319-13075-0_44
DO - 10.1007/978-3-319-13075-0_44
M3 - Conference contribution
AN - SCOPUS:84945186441
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 553
EP - 564
BT - Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
A2 - Ahn, Hee-Kap
A2 - Shin, Chan-Su
PB - Springer Verlag
T2 - 25th International Symposium on Algorithms and Computation, ISAAC 2014
Y2 - 15 December 2014 through 17 December 2014
ER -