Constructing near spanning trees with few local inspections
Name
Constructing near spanning trees.pdf
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Author(s)
Levi, Reut
Moshkovitz, Guy
Ron, Dana
Shapira, Asaf
Rubinfeld, Ronitt
Date Issued
January 2017
Journal
Random Structures and Algorithms
Publisher
Wiley Blackwell
Citation
Levi, Reut et al. “Constructing near Spanning Trees with Few Local Inspections.” Random Structures & Algorithms 50.2 (2017): 183–200.
Version
Original manuscript
Abstract
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph math formula consisting of math formula edges (for a prespecified constant math formula), where the decision for different edges should be consistent with the same subgraph math formula. Can this task be performed by inspecting only a constant number of edges in G? Our main results are:
We show that if every t-vertex subgraph of G has expansion math formula then one can (deterministically) construct a sparse spanning subgraph math formula of G using few inspections. To this end we analyze a “local” version of a famous minimum-weight spanning tree algorithm.
We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3-regular graphs of high girth, in which every t-vertex subgraph has expansion math formula. We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/rsa.20652
