Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
Sub-linear distributed algorithms for sparse certificates and biconnected components
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Fault-Tolerant Geometric Spanners
Discrete & Computational Geometry
FLSS: a fault-tolerant topology control algorithm for wireless networks
Proceedings of the 10th annual international conference on Mobile computing and networking
Distributive graph algorithms Global solutions from local data
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Connectivity Service for Mobile Ad-Hoc Networks
SASOW '08 Proceedings of the 2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshops
Keeping mobile robot swarms connected
DISC'09 Proceedings of the 23rd international conference on Distributed computing
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Local distributed algorithms can only gather sufficient information to identify local graph traits, that is, properties that hold within the local neighborhood of each node. However, it is frequently the case that global graph properties (connectivity, diameter, girth, etc) have a large influence on the execution of a distributed algorithm. This paper studies local graph traits and their relationship with global graph properties. Specifically, we focus on graph k-connectivity. First we prove a negative result that shows there does not exist a local graph trait which perfectly captures graph k-connectivity. We then present three different local graph traits which can be used to reliably predict the k-connectivity of a graph with varying degrees of accuracy. As a simple application of these results, we present upper and lower bounds for a local distributed algorithm which determines if a graph is k-connected. As a more elaborate application of local graph traits, we describe, and prove the correctness of, a local distributed algorithm that preserves k-connectivity in mobile ad hoc networks while allowing nodes to move independently whenever possible.