Generalized Steiner problem in series-parallel networks
Journal of Algorithms
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On the complexity of distributed network decomposition
Journal of Algorithms
IEEE Transactions on Parallel and Distributed Systems
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Introduction to Distributed Algorithms
Introduction to Distributed Algorithms
On colorings of squares of outerplanar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed Computing: Fundamentals, Simulations and Advanced Topics
Distributed Computing: Fundamentals, Simulations and Advanced Topics
On finding an ear decomposition of an undirected graph distributively
Information Processing Letters
A self-stabilizing algorithm for maximal 2-packing
Nordic Journal of Computing
Distance- k knowledge in self-stabilizing algorithms
Theoretical Computer Science
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Distributed (δ+1)-coloring in linear (in δ) time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weak graph colorings: distributed algorithms and applications
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
A memory efficient self-stabilizing algorithm for maximal k-packing
SSS'06 Proceedings of the 8th international conference on Stabilization, safety, and security of distributed systems
Self-stabilizing algorithms for {k}-domination
SSS'03 Proceedings of the 6th international conference on Self-stabilizing systems
Frequent subgraph mining in outerplanar graphs
Data Mining and Knowledge Discovery
Efficient transformation of distance-2 self-stabilizing algorithms
Journal of Parallel and Distributed Computing
A self-stabilizing algorithm to maximal 2-packing with improved complexity
Information Processing Letters
A self-stabilizing algorithm for optimally efficient sets in graphs
Information Processing Letters
A Self-stabilizing Algorithm for the Maximal 2-packing in a Cactus Graph
IPDPSW '12 Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum
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In this paper, we present a deterministic distributed algorithm that computes the maximal 2-packing set in a geometric outerplanar graph. In a geometric outerplanar graph, all the vertices have location coordinates in the plane and lie on the boundary of the graph. Our algorithm consists of three phases. First, it elects a vertex as the leader. Second, it explores the graph to determine relevant information about the structure of the input graph. Third, with this information, it computes a maximal 2-packing set. When the input graph is a ring, the algorithm computes a maximum 2-packing set. The execution time of this algorithm is O(n) steps and it uses O(nlogn) messages. This algorithm does not require knowledge of the size of the input graph. To the best of our knowledge, this is the first deterministic distributed algorithm that solves such a problem for a geometric outerplanar graph in a linear number of steps.