TY - GEN
T1 - Sublinear Time Shortest Path in Expander Graphs
AU - Alon, Noga
AU - Grønlund, Allan
AU - Jørgensen, Søren Fuglede
AU - Larsen, Kasper Green
N1 - Publisher Copyright:
© Noga Alon, Allan Grønlund, Søren Fuglede Jørgensen, and Kasper Green Larsen.
PY - 2024/8
Y1 - 2024/8
N2 - Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case. However, several works have shown how to solve this problem in sublinear time in expectation when the input graph is drawn from one of several classes of random graphs. In this work, we extend these results by giving sublinear time shortest path (and short path) algorithms for expander graphs. We thus identify a natural deterministic property of a graph (that is satisfied by typical random regular graphs) which suffices for sublinear time shortest paths. The algorithms are very simple, involving only bidirectional breadth first search and short random walks. We also complement our new algorithms by near-matching lower bounds.
AB - Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case. However, several works have shown how to solve this problem in sublinear time in expectation when the input graph is drawn from one of several classes of random graphs. In this work, we extend these results by giving sublinear time shortest path (and short path) algorithms for expander graphs. We thus identify a natural deterministic property of a graph (that is satisfied by typical random regular graphs) which suffices for sublinear time shortest paths. The algorithms are very simple, involving only bidirectional breadth first search and short random walks. We also complement our new algorithms by near-matching lower bounds.
KW - Breadth First Search
KW - Expanders
KW - Graph Algorithms
KW - Shortest Path
UR - http://www.scopus.com/inward/record.url?scp=85203361835&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.MFCS.2024.8
DO - 10.4230/LIPIcs.MFCS.2024.8
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AN - SCOPUS:85203361835
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 49th International Symposium on Mathematical Foundations of Computer Science, MFCS 2024
A2 - Kralovic, Rastislav
A2 - Kucera, Antonin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 49th International Symposium on Mathematical Foundations of Computer Science, MFCS 2024
Y2 - 26 August 2024 through 30 August 2024
ER -