@MISC{P_branchingrandom, author = {Chinmoy Dutta Gopal P}, title = {Branching Random Walks on Graphs}, year = {} }

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Abstract

We study a new distributed randomized information propagation mechanism in networks that we call a branching random walk (BRW). BRW is a generalization of the well-studied “standard ” random walk which is a fundamental primitive useful in a wide variety of network applications ranging from token management and load balancing to search, routing, information propagation and gossip. BRW is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. For instance, this could be a node that has a piece of data, rumor, or a virus. In a BRW, in any step, each active node chooses k random neighbors to become active for the next step. A node is active for step t + 1 only if it is chosen by an active node in step t. This results in a branching type process in the underlying network which has interesting properties that are strikingly different from the standard random walk, which is equivalent to BRW with branching factor k = 1. Similar to the standard random walk, we focus on the cover time, which is the the number of steps for the walk to reach all the nodes and the partial cover time, which is the number of steps needed for the walk to reach at least a constant fraction of the nodes. We derive almost-tight bounds on cover time and partial cover time in expander graphs, an important