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Tarry vs Awerbuchs. Shawn Biesan. Background. Tarry’s Transversal Algorithm Initiator forwards token to one of neighbors, each neighbor forwards token to all other nodes and when done returns token Complexity: 2 * [number of edges] Constructs spanning tree Awerbuchs
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Tarry vsAwerbuchs Shawn Biesan
Background • Tarry’s Transversal Algorithm • Initiator forwards token to one of neighbors, each neighbor forwards token to all other nodes and when done returns token • Complexity: 2 * [number of edges] • Constructs spanning tree • Awerbuchs • Node notifies neighbors that it is visited by sending <vis> so tokens are never sent over frond edges • Time complexity: 4 * [number of nodes] – 2 • Constructs spanning tree • Time Complexity - Number of causally related messages
Experiment • 2 experiments comparing time complexities • Varying number of processes • 5-50, varied by 5 node increments • Varying density of partially connected graph • Probability that there is an edge between two nodes varies from 30%-100%(fully connected) by increments of 10%, denoted as p • Graph must be connected, if it isn’t the graph is regenerated until the created graph is connected • Number of nodes is fixed at 10 • Each data point is the result of averaging 5 trials
Expected Results • Tarrys time complexity will be better for sparse graphs • Its time complexity depends on number of edges(2E) whereas Awebuchs depends on the number of nodes (4N -2) • As p increases Awerbuchswill improve until it has a better time complexity than Tarrys • Greatest difference between them for fully connected graphs
Interpretation • Awerbuchsis indeed better than Tarrys as nodes scale in a completely connected graph • The number of edges grows much faster than nodes ( #edges= (N(N-1))/2 ) • Tarrys algorithm is indeed better for sparse graphs up until about p=0.4 • Expected value of number edges when p=0.4 is 18 so it matches up with theoretical
Code • Most difficult/interesting part of the code was related to how the simulation engine was made • Each new algorithm must implement a specific interface in order to be used • Made adding new algorithms less painful
Conclusions And Future Work • In general Tarry’s algorithm should be used for sparse graphs with small number of nodes, otherwise use Awerbuchs • Easier to implement • Sends less messages – No overhead of <VIS> and <ack> messages • Future Work • Explore different topologies • Explore Message Complexity deeper
Questions? • Thank you