Rumor Spreading on Random Regular Graphs and Expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. The performance of the push model has been studied for several types of networks. One particular result [14] addressing its robustness and efficiency is the following. Suppose that the network is a random graph, where each edge appears independently with probability p = (ln n n ), i.e., the average degree is significantly larger that ln n. Then, regardless of the actual value of p, the broadcast time is (1 + o(1))C ln n, where C = 1 ln 2 + 1, with probability 1 - o(1). In other words, the number of rounds needed to broadcast the information is essentially the same on the complete graph, and on almost ...

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: Nikolaos Fountoulakis, Konstantinos Panagiotou
• Keywords: Algorithms, APPROX 2010, Ln N, Push Model, Well-studied Push Model