A Recursive, Distributed Minimum Spanning Tree Algorithm for Mobile Ad Hoc Networks

We introduce a recursive (“anytime”) distributed algorithm that iteratively restructures any initial spanning tree of a weighted graph towards a minimum spanning tree while guaranteeing at each successive step a spanning tree shared by all nodes that is of lower weight than the previous. Each recursive step is computed by a different active node at a computational cost at most quadratic in the total number of nodes and at a communications cost incurred by subsequent broadcast of the new edge set over the new spanning tree. We show that a polynomial cubic in the number of nodes bounds the worst case number of such steps required to reach a minimum spanning tree and, hence, the number of broadcasts along the way. We conjecture that the distributed, anytime nature of this algorithm is particularly suited to tracking minimum spanning trees in (sufficiently slowly changing) mobile ad hoc networks. Disciplines Electrical and Computer Engineering | Engineering | Systems Engineering Comments For more information: Kod*Lab This presentation is available at ScholarlyCommons: http://repository.upenn. edu/ese_papers/699 RSS2014Workshop on Communication-awareRobotics: NewTools forMulti-Robot Networks, AutonomousVehicles, and Localization A Recursive, Distributed Minimum Spanning Tree Algorithm for Mobile Ad Hoc Networks Omur Arslan Department of Electrical and Systems Engineering, University of Pennsylvania Philadelphia, PA 19104 Email: omur@seas.upenn. edu Daniel E. Koditschek Department of Electrical and Systems Engineering, University of Pennsylvania Philadelphia, PA 19104 Email: kod@seas.upenn. edu Abstract—We introduce a recursive (“anytime”) distributed algorithm that iteratively restructures any initial spanning tree of a weighted graph towards a minimum spanning tree while guaranteeing at each successive step a spanning tree shared by all nodes that is of lower weight than the previous. Each recursive step is computed by a different active node at a computational cost at most quadratic in the total number of nodes and at a communications cost incurred by subsequent broadcast of the new edge set over the new spanning tree. We show that a polynomial cubic in the number of nodes bounds the worst case number of such steps required to reach a minimum spanning tree and, hence, the number of broadcasts along the way. We conjecture that the distributed, anytime nature of this algorithm is particularly suited to tracking minimum spanning trees in (sufficiently slowly changing) mobile ad hoc networks.We introduce a recursive (“anytime”) distributed algorithm that iteratively restructures any initial spanning tree of a weighted graph towards a minimum spanning tree while guaranteeing at each successive step a spanning tree shared by all nodes that is of lower weight than the previous. Each recursive step is computed by a different active node at a computational cost at most quadratic in the total number of nodes and at a communications cost incurred by subsequent broadcast of the new edge set over the new spanning tree. We show that a polynomial cubic in the number of nodes bounds the worst case number of such steps required to reach a minimum spanning tree and, hence, the number of broadcasts along the way. We conjecture that the distributed, anytime nature of this algorithm is particularly suited to tracking minimum spanning trees in (sufficiently slowly changing) mobile ad hoc networks.